If , verify that A 2 – 4 A + I = O, where and . Hence, find A – 1 .

Question

Philoid · Accepted Answer

A² =

=

4A =

I =

Now, A² – 4 A + I =

=

Hence, =

Now, A² – 4 A + I = 0

A.A – 4A = – I

Multiply by A ^{– 1} both sides

A.A(A ^{– 1}) – 4A A ^{– 1} = – IA ^{– 1}

AI – 4I = – A ^{– 1}

A ^{– 1 =} 4I – A =

A ^{– 1} =

If , verify that A2 – 4 A + I = O, where and . Hence, find A – 1.