Find the inverse of each of the following matrices and verify that A ^{– 1} A = I₃.

Question

Find the inverse of each of the following matrices and verify that A – 1 A = I 3 .

Philoid · Accepted Answer

|A| =

= 2(8 – 7) – 3(6 – 3) + 1(21 – 12)

= 2 – 9 + 9

= 2

Hence, A ^{– 1} exists

Cofactors of A are:

C₁₁ = 1 C₂₁ = 1 C₃₁ = – 1

C₁₂ = – 3 C₂₂ = 1 C₃₂ = 1

C₁₃ = 9 C₂₃ = – 5 C₃₃ = – 1

adj A =

=

So, adj A =

Now, A ^{– 1} =

Also, A ^{– 1}.A =

=

Hence, A ^{– 1}.A = I

Find the inverse of each of the following matrices and verify that A – 1 A = I3.