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If A=[(i,0), (0,i)],\ n in N , then A^(...

If `A=[(i,0), (0,i)],\ n in N` , then `A^(4n)` equals `[(0,i), (i,0)]` (b) `[(0 ,0) ,(0, 0)]` (c) `[(1, 0) ,(0, 1)]` (d) `[(0,i) ,(i,0)]`

A

`{:[(0,i),(i,0)]:}`

B

`{:[(0,0),(0,0)]:}`

C

`{:[(1,0),(0,1)]:}`

D

`{:[(0,i),(i,0)]:}`

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `{:A=[(i,0),(0,i)]:}`
Clearly, A is a diagonal matrix. Therefore,`A^(4n)` is also a diagonal matrix such that
`A^(4n)={:[(i^(4n),0),(0,i^(4n))]=[(1,0),(0,1)]:}`
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