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If matrix `A` is given by `A=|[6, 11], [2, 4]|` , then the determinant of `A^(2005)-6A^(2004)` is a. `2^(2006)` b. `(-11)2^(2005)` c. `-2^(2005)` d. `(-9)2^(2004)`

A

`2^(2006)`

B

`(-11)2^(2005)`

C

`-2^(2005).7`

D

`(-9) 2^(2004)`

Text Solution

Verified by Experts

The correct Answer is:
B
`|A^(2005)-6A^(2004)|=|A|^(2004)|A-6I|`
`=2^(2004)|(0,11),(2,-2)|=(-22) 2^(2004)=(-11) (2)^(2005)`
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