If A= [ array lll 2 & 1 & 3 3 & 1 & 2 1 & 2 & 3 array ] and I is an identity by matrix of order 3 3 then A( adj A)=

Step-by-step solution

The property of the adjoint of a matrix states that A( adj A) = |A| I , where |A| is the determinant of matrix A and I is the identity matrix of the same order. Given A = bmatrix 2 & 1 & 3 3 & 1 & 2 1 & 2 & 3 bmatrix , we calculate the determinant |A| by expanding along the first row: |A| = 2(1 3 - 2 2) - 1(3 3 - 2 1) + 3(3 2 - 1 1) |A| = 2(3 - 4) - 1(9 - 2) + 3(6 - 1) |A| = 2(-1) - 1(7) + 3(5) |A| = -2 - 7 + 15 = 6 Therefore, A( adj A) = 6I . Answer: 6 I