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If the matrix A={:[(5,-3),(5,-3)]:}," th...

If the matrix `A={:[(5,-3),(5,-3)]:}," then "A^(n+1)` = ________ .

A

`{:[(5,-3),(5,-3)]:}`

B

`{:[(5,3),(5,3)]:}`

C

`2^(n){:[(5,-3),(5,-3)]:}`

D

`2^(n+1){:[(5,-3),(5,-3)]:}`

Text Solution

Verified by Experts

The correct Answer is:
C
`A={:[(5,-3),(5,-3)]:}`
`A^(2)={:[(5,-3),(5,-3)]:}{:[(5,-3),(5,-3)]:}`
`{:[(25-15,-15+9),(25-15,-15+9)]:}`
`{:[(10,-6),(10,-6)]:}=2{:[(5,-3),(5,-3)]:}`
`A^(3)=A^(2)*A`
`{:[(10,-6),(10,-6)]:}{:[(5,-3),(5,-3)]:}`
`{:[(50-30,-30+18),(50-30,-30+18)]:}={:[(20,-12),(20,-12)]:}`
`=4{:[(5,-3),(5,-3)]:}=2^(2){:[(5,-3),(5,-3)]:}`
`A^(n+1)=2^(n){:[(5,-3),(5,-3)]:}`.
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