Find the inverse of the matrix and show that aA ^{– 1} = (a² + bc + 1) I – aA.

A =

Now, |A| = bc =

Hence, A ^{– 1} exists.

Cofactors of A are

C₁₁ = C₁₂ = – c

C₂₁ = – b C₂₂ = a

Since, adj A =

(adj A) =

=

Now, A ^{– 1} = .adj A

A ^{– 1} = .

A ^{– 1} =

To show. aA ^{– 1} = (a² + bc + 1) I – aA.

LHS aA ^{– 1} = a

=

RHS (a² + bc + 1) I – aA =

=

Hence, LHS = RHS