If , Show that A² = A^–1.

|A| =

|A| = – 1(0 – 1) – 2(0) + 0

= 1 – 0 + 0

|A| = 1

A =

A² = A.A =

=

=

Cofactors of A are:

C₁₁ = – 1 C₂₁ = 0 C₃₁ = 2

C₁₂ = 0 C₂₂ = 0 C₃₂ = 1

C₁₃ = – 1 C₂₃ = 1 C₃₃ = 1

adj A =

=

So, adj A =

Now, A ^{– 1} =

Hence, A ^{– 1} = = A²