Verify that A3 – 6A2 + 9A – 4I = O and hence find A–1

Verify that A³ – 6A² + 9A – 4I = O and hence find A^–1

Solution :

Multiply A with A to get A²

 Multiply A² with A to get A³

We have  A³ – 6A² + 9A – 4I = O plug the value

Multiply equation by A^-1 to get A^-1

We get

 A³ A^-1  – 6A² A^-1  + 9A A^-1  – 4I A^-1  = O A^-1

Solve it we get

A² – 6A + 9I – 4 A^-1 = O

A² – 6A + 9I =4 A^-1

or

4 A^-1 = A² – 6A + 9I

Plug the values we get