If prove that for all n ∈ N.

Given :

Matrix A is of order 2 2.

To prove :

Proof :

A =

Let us assume that the result holds for A^{n – 1}

A^{n – 1} =

We need to prove that the result holds for Aⁿ by mathematical induction .

Aⁿ = A^{n – 1} × A = =

Aⁿ = =

Aⁿ =