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Question

Let A be a nth order square matrix and matrix B be its adjoint, then |AB+KIn| is equal to (where K is a scalar quantity)

A
(|A|+K)n2
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B
(|A|+K)n
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C
(|A|+K)n1
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D
(|A|+K)1
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Solution

The correct option is B (|A|+K)n
We have, AB=A(adjA)=|A|In

AB+KIn=|A|In+KIn

AB+KIn=(|A|+K)In

|AB+KIn|=|(|A|+K)In| (|aIn|=an)

|AB+KIn|=(|A|+K)n

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