Is that an inerrant belief or a belief based upon Protestant tradition? In the first century there was a Pharisee canon, a Sadducee canon, an Essene canon and the Septuagint canon. Which of these represented the true and proper canon agreed to by all Jews "in General" and which by Greek speaking Jews?
The Protestants of the 16th century knew almost nothing about the Judaism of the First Century and assumed that the Jews they knew were the same as the Pharisees Our Lord knew,
No, they did not all have canons. And none proclaimed the Apocrypha to be an inspired part of a canon.
“Josephus writes that the canon consisted of the five books of Moses, thirteen of the Prophets and four of what he referred to as hymns to God and precepts for human life. It is clear that this perspective was one held for a long time by the Jews, who considered these twenty-two books alone to be of divine origin and were careful to preserve the integrity and number of them. In fact, so great was their veneration of these books, they were willing to die for them. Surely, such a commitment implies a conviction that these books alone were truly canonical. In addition, it is clear that the canon referred to by Josephus did not include the books of the Apocrypha, and that he considered the canon to be closed. He states that the twenty-two books were written in the specific span of time from Moses to Artaxerxes and no books written after this time were considered inspired. He mentions other books written after the prophets, which were not considered by the Jews to carry the same authority, that is, they were not inspired and were, therefore, not canonical. This is a clear reference to a number of the Apocryphal books. John Wenham summarizes the importance of Josephus and his writings:
Josephus, born about AD 37, was perhaps the most distinguished and most learned Jew of his day. His father was a priest and his mother was descended from the Maccabean kings. Given the best possible education, he proved to be something of a prodigy…What is particularly interesting about the statement of Josephus is the clear distinction between the canonical books which were completed in the time of Artaxerxes, and those written later which were not considered worthy of like credit ‘because the exact succession of the prophets ceased’. The idea evidently is that the canonical books were either written (or accredited) by the prophets, but that when the prophetical era was over, no more books suitable for the Canon were written…Josephus commits himself to a fairly precise date for the closing of the Canon. Artaxerxes Longimanus reigned for forty years, 465 to 425 BC. Ezra came to Jerusalem in the seventh, and Nehemiah in the twentieth, year of his reign (Ez. 7:1, 8; Ne. 2:1). In addition to Josephus there are several other witnesses who point to the time of Ezra and Nehemiah, with occasionally a reference to the ministries of Haggai, Zechariah and Malachi, as the time of the collection, completion and recognition of the Old Testament Canon.28
F.F. Bruce explains how the precise books can be inferred from Josephus’ statements:
When Josephus speaks of twenty-two books, he probably refers to exactly the same documents as the twenty-four of the traditional Jewish reckoning, Ruth being counted as an appendix to Judges and Lamentations to Jeremiah. His three divisions might be called the Law, the Prophets and the Writings. His first division comprises the same five books as the first division of the traditional arrangement. But his second division has thirteen books, not eight, the additional five being perhaps Job, Esther, Daniel, Chronicles and Ezra-Nehemiah. The four books of the third division would then be Psalms, Proverbs, Ecclesiastes and Song of Songs. It is impossible to be sure, because he does not specify the books of the three divisions one by one. It is unlikely that Josephus’ classification of the books was his own; he probably reproduces a tradition with which he had been familiar for a long time, having learned it either in the priestly circle into which he was born or among the Pharisees with whose party he associated himself as a young man.29
Ryle offers this additional observation:
He records a test of their canonicity. He mentions the standard which, apparently, in current Jewish opinion, all books satisfied that were included in the Canon. No historical writings, it seems, belonged to it which were deemed to have been composed later than the reign of Ahasuerus. The mention of this particular limit seems to be made expressly with reference to the book of Esther, in which alone the Artaxerxes of Josephus (the Ahasuerus of the Hebrew book of Esther) figures. Thus we learn that a popularly accepted test, that of date of composition, however erroneously applied, determined the question of canonicity. In the first cent. A.D., the impression prevailed that the books of the Canon were all ancient, that none were more recent than Ahasuerus, and that all had long been regarded as canonical. The same limit of date, although not so clearly applied to the poetical books, was, in all probability, intended to apply equally to them, since they combined with the books of the prophets to throw light upon the same range of history. That such a standard of canonicity as that of antiquity should be asserted, crude as it may seem, ought to be sufficient to convince us that the limits of the Canon had for a long time been undisturbed.30
Jerome, famous for translating the Hebrew Old Testament into Latin, was intent on translating only those books deemed canonical by the Jews. He not only bears witness to the threefold traditional classification of the Hebrew Bible, but also to which books comprised each category. His list is essentially the same as that inferred from Josephus’ writings. The specific books he lists are:
1) The Law of Moses: Genesis, Exodus, Leviticus, Numbers and Deuteronomy.
2) The Prophets: Joshua, Judges, Ruth, I & II Samuel, I & II Kings, Isaiah, Jeremiah, Ezekiel and the twelve minor prophets.
3) The Hagiographa: Job, Psalms, Proverbs, Ecclesiastes, Song of Solomon, Daniel, Chronicles, Ezra-Nehemiah and Esther.31”
“Josephus divided the books into three sections: the Law of Moses, the Prophets and what he called ‘hymns to God and precepts for human life,’ also referred to as the Writings or the Hagiographa.”
http://christiantruth.com/articles/Apocryphapart1.html
44 Then he said to them, “These are my words that I spoke to you while I was still with you, that everything written about me in the Law of Moses and the Prophets and the Psalms must be fulfilled.” - Jesus Christ
Notice Jesus gives 3 sections, as did Josephus: “the Law of Moses and the Prophets and the Psalms” or “the Law of Moses, the Prophets and what he called ‘hymns to God and precepts for human life,’.
When Jesus said, ““34 Therefore I send you prophets and wise men and scribes, some of whom you will kill and crucify, and some you will flog in your synagogues and persecute from town to town, 35 so that on you may come all the righteous blood shed on earth, from the blood of righteous Abel to the blood of Zechariah the son of Barachiah, whom you murdered between the sanctuary and the altar”, he also described the canon.
In the Jewish scriptures, the blood of Zechariah the son of Barachiah (2 Chronicles 24) came at the end. Thus Able to Zechariah the son of Barachiah covered from the first boo0k in order to the last book, in order. Front to back. The statement of Jesus only makes sense if the Jewish canon, and the order of the books, was established, known and accepted.
http://en.wikipedia.org/wiki/Tanakh#Ketuvim