If . Verify that A 3 – 6A 2 + 9A – 4I = O and hence fid A – 1 .

Question

Philoid · Accepted Answer

A =

A³ = A².A

A² =

=

A².A =

=

Now, A³ – 6A² + 9A – 4I

=

Thus, A³ – 6A² + 9A – 4I

Now, (AAA) A ^{– 1}. – 6(A.A) A ^{– 1} + 9.A A ^{– 1} – 4I.A ^{– 1} = 0

A² – 6A + 9I = 4A ^{– 1}

= A ^{– 1} =

Now,

=

Hence, A ^{– 1} =