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Question

If P=[aij]n×n be any matrix and it is non singular matrix. If |P| = |Q| = 1 and adj B = A, then adj(Q1BP1) is

A
QAP
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B
PAQ
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C
AQP
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D
PQA
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Solution

The correct option is B PAQ
|P| = 1 = |Q| and adj B = A
We know that (adj P1)=(adj P)1
(adj Q1)=(adj Q)1 adj(Q1BP1)=(adj P1)adj B adj Q1=(adj P1) adj B (adj Q)1=(P1)1A(Q1)1
= PAQ

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