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Question

Matrices A and B satisfy AB=B1, where B=[2120], then find without finding A1, the matrix X satisfying A1XA=?

A
B
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B
B2
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C
A
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D
None of these
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Solution

The correct option is A B
Given, A1XA=B

AA1XA=AB

IXA=AB

XAB=AB2

XAB=I since [AB=B1AB2=I]

XAB2=B

XI=B

X=B

Hence option A is the answer.

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