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Let A be an nth-order square matrix and ...

Let `A` be an nth-order square matrix and `B` be its adjoint, then `|A B+K I_n|` is (where `K` is a scalar quantity) a. `(|A|+K)^(n-2)` b. `(|A|+K)^n` c. `(|A|+K)^(n-1)` d. none of these

A

`(|A|+K)^(n-2)`

B

`(|A|+K)^(n)`

C

`(|A|+K)^(n-1)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `AB=A ("adj A")=|A| I_(n)`
`:. AB+KI_(n)=|A|I_(n)+KI_(n)`
`=(|A|+K)I_(n)`
`implies |AB+KI_(n)|=|(|A|+K)I_(n)|" "( :' |alphaI_(n)|=alpha^(n))`
`=(|A|+K)^(n)`
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