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 = 3 C₂₁ = – 1 C₃₁ = – 1

C₁₂ = – 15 C₂₂ = 7 C₃₂ = – 5

C₁₃ = 4 C₂₃ = – 2 C₃₃ = 2

adj A =

=

adj A =

Now, (adj A).A =

=

=

Also, |A|.I =

= [2(3 – 0) + 0(15 – 0) – 1(5 – 1)]

= (6 – 4)

=

Then, A.(adj A) =

=

=

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