If `A=d i ag\ (a\ \ b\ \ c)` , show that `A^n=d i ag\ (a^n\ \ b^n\ \ c^n)` for all positive integer `n` .

Explanation

`A=diag(a, b,c)`

`A=[[a, 0, 0], [0, b, 0], [0, 0,c]]`

`A^n=diag(a^n, b^n, c^n)`

`=[[a^n, 0, 0], [0, b^n, 0], [0, 0, c^n]]`

Using mathematical induction,

when `n=1`

`A^N=[[a^1, 0, 0], [0, b^1, 0], [0, 0, c^1]]`

`A^N=A`
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