Only if you impose the constraint that the permutation matrix mapping plaintext to ciphertext has only zeros on the main diagonal. (Which is generally the case with good popular cryptograms.) Yes, element {3,3} is indeed 1. This constraint is actually a cryptological weakness, one that greatly aided breaking the German Enigma cipher.
And the ‘sudden’ downfall of Yamamoto
https://www.thoughtco.com/operation-vengeance-death-yamamoto-2360538