Q. 34.2( 31 Votes )

Verify A (adj A)

Answer :

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 = -6, A12 = 4, A21 = -3, A22 = 2.


Adj A =


=


So LHS = A(AdjA) =


Also AdjA(A) =


Determinant of A = |A| = 2(-6)-(3)(-4) = 0


So RHS = |A|I = 0


Hence A(AdjA) = AdjA(A) = |A|I = 0 {hence proved}


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