Let A = 0 1 0 1 0 0 0 0 1 . Then the number of 3 × 3 matrices B with entries from the set 1 , 2 , 3 , 4 , 5 and satisfying A B = B A is ________.

Step-by-step solution

Let, the matrix B = a b c d e f g h i ∵   A B = B A 0 1 0 1 0 0 0 0 1 a b c d e f g h i = a b c d e f g h i 0 1 0 1 0 0 0 0 1 ⇒   d e f a b c g h i = b a c e d f h g i On equating the matrices, we get ⇒ d = b ,   e = a ,   f = c ,   g = h ∴ Matrix B = a b c b a c g g i No. of ways of selecting each of a ,   b ,   c ,   g ,   i from the set 1 ,   2 ,   3 ,   4 ,   5 are 5 . Thus, the total number of ways are = 5 × 5 ×