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If A=[(1,0),(1,1)] and I=[(1,0),(0,1)] t...

If `A=[(1,0),(1,1)] and I=[(1,0),(0,1)]` then which one of the following holds for all `nge1` by the principle of mathematical induction?

A

`A^(n) = nA+(n-1) I`

B

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

C

`A^(n) = nA-(n-1) I`

D

None of this

Text Solution

Verified by Experts

The correct Answer is:
C
`A^(2) = [[1,0],[1,1]] [[1,0],[1,1]] =[[1,0],[2,1]]`
`A^(3) = [[1,0],[2,1]] [[1,0],[1,1]] =[[1,0],[3,1]]`
`A^(n) = [[1,0],[n,1]]`
`nA = [[n,0],[n,n]], (n-1) I = [[n-1,0],[0,n-1]]`
`nA-(n-1)I= [[1,0],[n,1]]=A^(n)`
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