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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+5)`

B

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

C

`3A^(2)-2A-5I`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Let A be a matrix such that `3A^(3) + 2A^(2) + 5A + I = 0`
Post multiply by `A^(-1)` on both sides, we get `3A^(3) A^(-1) + 2A^(2)A^(-1) + 5AA^(-1) + IA^(-1) = 0`
`rArr 3A^(2) + 2A + 5I + A^(-1) = 0`
`rArr A^(-1) =-(3A^(2)+2A+5I)`
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