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

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

Text Solution

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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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