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If a matrix A is such that 3A^3 +2A^2+5A...

If a matrix `A` is such that `3A^3 +2A^2+5A+I= 0`, then `A^(-1)` is equal to

A

`3A^(2)+2A+5l`

B

`-(3A^(2)+2A+5l)`

C

`-(3A^(2)+A+5l)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given `3A^(3)+2A^(2)+5A+l=0`
Pre multiplying both sides by `A^(-1)` we get
`3A^(-1)A^(3)+2A^(-1)A^(2)+5A^(-1)A+A^(-1)l=A^(-1)O`
`implies3(A^(-1)A)A^(2)+2(A^(-1)A)A+5A^(-1)A+A^(-1)=0`
`implies3A^(2)+2A+5l+A^(-1)=0`
`impliesA^(-1)=-(3A^(2)+2A+5l)`
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