Question

How to do ii)
Deduce A^-1 = A^2 based on A^3=I

Answer 1

Multiply by
`A^(-1)` on the right of both sides of
`A^3=I`, then use the fact that matrix multiplication is associative.

If
`A^3=I`, then

`A^3A^(-1)=IA^(-1)`

`A^2(AA^(-1))=A^(-1)`

`A^2I=A^(-1)`

`\implies A^2=A^(-1)`