Find the adjoint of each of the following Matrices and Verify that (adj A) A = |A| I = A (adj A)

Verify that (adj A) A=|A| I=A (adj A) for the above matrices.

A =

Cofactors of A

C₁₁ = 2 C₂₁ = 3 C₃₁ = – 13

C₁₂ = – 3 C₂₂ = 6 C₃₂ = 9

C₁₃ = 5 C₂₃ = – 3 C₃₃ = – 1

adj A =

=

adj A =

Now, (adj A).A =

=

=

Also, |A|.I = = [1(3 – 1) – 2(2 + 1) + 5(2 + 3)]

= (21)

=

Then, A.(adj A) =

=

=

Hence, (adj A).A = |A|.I = A(adj A)