Important to also note that the Yamato (sunk in April 1945 during its Kamikazi mission against US forces at Okinawa) and the Musachi (sunk in October 1944 during the Battle of the Sibuyan Sea during the overall Battle of Leyte Gulf) were never his by US Navy battleship rifle fire during the war.
They were both sunk by US Naval aviation.
There was a third, the Shinano, which was converted to a carrier while building in 1942 that was sunk in November 1944 by a US submarine on its maiden voyage.
A fourth, which was never named, was only 30% complete when it as canceled well before the end of the war, and broken up in place by the Japanese during the war.
The armor pictured in that photo above is a piece of 26” turret armor off of one of the Yamato class that the USN salvaged later for testing purposes
Yamato blows up after severe punshiment by US Naval aircraft on April 7, 1945:

Musashi being hammered on Otober 24, 1944 by US Naval aircraft:

The converted Yamato class battleship, the Shinano (which was the largest carrier ever built until the US Navy first super carrier (the Frrestal) displacing 70,000 tons), underway during her sea trials. She would be sunk on November 28, 1944 on her initial cruise after being commissioned.

The Shanino took four torpedos and that was enough to sink her, which was a relatively light number of hits when compared to what it took to sink the other Yamato class ships. It was later determined that she had serious flaws in the welding for her watertight integrity, which probably ccurred during her conversion to accunt for her sinking.
By comparison, the other two full battleships took an unbelievable amount of pounding to put them down.
The Musashi, on October 24, 1944, while crossing the Sibuyan Sea during the overasll Battle of Leyte Gulf, with ther sister ship Yamato, other battleships, numerous crusers and many destroyers, was attacked by US Naval aircraft.
She was attacked four different times between 10:30 AM and 2:00 PM. First by eight Gruman TBF Avenger Torpedo bombers. Then, and hour and a half later, by eight Helldiver dive bombers. Then, nine more Avenger Torpdo bombers attacked. Finally, twenty-nine more aircraft (Helldivers, Avengers, and Hellcats) attacked. All in all, she was attacked by 54 aircraft. She was hit by 19 torpedos and 17 bombs (13 bombs and 11 torpedos in the last large attack). Most all of the bombs were 500 lb bombs.
After first being hit at 10:30 AM, and all hits having registered by 2 PM, she still took anther 7 1/2 hours to sink, going down at 19:36 on October 24, 1944. Over 1,020 of her crew was lost.
The Yamato, on April , 1945, after being ordered to attack the large US Navl forces massed at Okinawa, and having been given enough fuel for only the one way trip...in other words on the largest Kamikazi mission of the war...was located and attacked by US Naval aircaft.
At 12:30 in the afternoon, US naval aircrat arrived and attacked the Japanese formation. Another group joined in at 13:00 PM and a third group came in at 13:40 PM> All in all, over 280 aircraft attacked the Yamato and her escorts. She was totally overwhelmed. She was hit by a confirmed 11 torpedos and 6 bombs, though it was reported that the total number was 13 torpedos and 8 bombs. Either way, it was enough. At 14:22, as she was settling and rolling over, her main magazine exploded, obliterating her (as shown above). Over 3,050 of her crew was killed in the attack.
All in all, the Japanese lost almost 4,100 sailors with the loss of these two battleships. They were the largest and most heavily armored battleships ever built. But they were n match for US Naval air power...partiularly when they had no air cover themselves. Their day was over.