If , find A – 1 and show that A – 1 = 1/2(A2 – 3I).

Question

Philoid · Accepted Answer

A = |A| = 0 – 1(0 – 1) + 1(1 – 0) = 0 + 1 + 1 = 2

Cofactors of A are:

C₁₁ = – 1 C₂₁ = 1 C₃₁ = 1

C₁₂ = 1 C₂₂ = – 1 C₃₂ = 1

C₁₃ = 1 C₂₃ = 1 C₃₃ = – 1

adj A =

=

So, adj A =

Now, A ^{– 1} =

A² – 3I =

=

Hence, A ^{– 1} = (A² – 3I)

If , find A ^{– 1} and show that A ^{– 1} = 1/2(A² – 3I).