If M= bmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 bmatrix , then what is the value of |M| ,| adj M| ?

Step-by-step solution

Given M = bmatrix 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 bmatrix The determinant of the diagonal matrix M is |M| = 2 2 2 = 8 . For a square matrix of order n , the determinant of its adjoint is given by | adj M| = |M|^ n-1 . Since the order of M is n = 3 , we have | adj M| = |M|³⁻¹ = |M|^2 . The required value is |M| , | adj M| = |M| |M|^2 = |M|^3 . Substituting |M| = 8 , we get 8^3 = 512 . Answer: 512