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If A={:[(7,0),(0,7)]:}," then find "A^(n...

If `A={:[(7,0),(0,7)]:}," then find "A^(n)(ninN)` ________ .

A

`{:[(7,0),(0,7)]:}`

B

`{:[(7^(n),0),(0,7^(n))]:}`

C

`{:[(7,7^(n)),(0,7^(n))]:}`

D

`{:[(0,7^(n)),(7^(n),0)]:}`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `A={:[(7,0),(0,7)]:}`
`A-7={:[(1,0),(0,1)]:}`
`A=7I`
`A^(n)=7^(n)I^(n)`
`A^(n)=7^(n)I(becauseI^(n)=I)`
`=7^(n){:[(1,0),(0,1)]:}`
`={:[(7^(n),0),(0,7^(n))]:}`.
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