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If A=[[3,-4],[1,-1]], then prove that A^...

If `A=[[3,-4],[1,-1]]`, then prove that `A^n=[[1+2n,-4n],[n,1-2n]]`, where n is any positive integer.

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Given `A=[[3,-4],[1,-1]]`,
To prove: `A^n=[[1+2n,-4n],[n,1-2n]]`,
Let n=1:
`A^1=[[1+2,-4],[1,1-2]]`
`=>[[3,-4],[1,-1]]=A`
The result is true for n=1
let `n=k`
`A^k=[[1+2k,-4k],[k,1-2k]]`,
...
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