​ 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 AB = BA

Question

Let A = \(\begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}\). Then the number of 3 × 3 matrices B with entries from the set {1, 2, 3, 4, 5} and satisfying AB = BA is _______.

Answer 1

No. of ways of selecting a, b, c, g, i

= 5 × 5 × 5 × 5 × 5

= 5⁵ = 3125

∴ No. of Matrices B = 3125