Q27 of 74 Page 7

If , prove that A ^{– 1} = A^T.

A = A^T =

|A| = [ – 8(16 + 56) – 1(16 – 7) + 4( – 32 – 4)]

= – 81

Cofactors of A are:

C₁₁ = 72 C₂₁ = – 36 C₃₁ = – 9

C₁₂ = – 9 C₂₂ = – 36 C₃₂ = 72

C₁₃ = – 36 C₂₃ = – 63 C₃₃ = – 36

adj A =

So, adj A =

Now, A ^{– 1} =

Hence, A ^{– 1} = = A^T

Show that the matrix, satisfies the equation, A³ – A² – 3A – I₃ = O. Hence, find A^–1.

If . Verify that A³ – 6A² + 9A – 4I = O and hence fid A ^{– 1}.

If , show that A ^{– 1} = A³.

If , Show that A² = A^–1.

If , prove that A – 1 = AT.