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If A is a non-singular matrix such that ...

If `A` is a non-singular matrix such that `(A-2I)(A-4I)=0` , then `(A+``8``A^(-1))` = .....

A

`I`

B

0

C

`3I`

D

`6I`

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `|A|=ne0`
`impliesA^(-1)` is exists.
since, `(A-2I)(A-4I)=0`
`impliesA^(2)-A(4I)-2I(A)+8I*I=0`
`impliesA^(2)-4AI-2AI+8I=0`
`impliesA^(2)-8AI+8I=0`
`impliesA^(2)-6A+8I=0`
On pre multiply both sides by `A^(-1)`, we get
`A^(-1)A^(2)_6A^(-1)A+8A^(-1)I=0`
`impliesIA-6I+8A^(-1)=0`
`impliesA-6I+8A^(-1)=0impliesA+8A^(-1)=6I`
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