Verify A (adj A) = (adj A) A = |A|


Adjoint of the matrix A = [aij]n×n is defined as the transpose of the matrix [Aij]n×n where Aij is the co-factor of the element aij.

Let’s find the cofactors for all the positions first-


Here, A11 = 0, A12 = -11, A13 = 0, A21 = 3, A22 = 1, A23 = -1, A31 = 2, A32 = 8, A33 = 3.


Adj A =


=


So, LHS = A(AdjA) =


Also AdjA(A) =


Determinant of A = |A| = 11


So RHS = |A|I = .


Hence A(AdjA) = AdjA(A) = |A|I = {hence proved}


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