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Question

A is an involutory matrix given by A=⎡⎢⎣01−14−343−34⎤⎥⎦ then the inverse of A2 will be

A
2A
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B
A12
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C
A2
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D
A2
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Solution

The correct option is B A12
Given A to be involutory matrix, then according to the definition of involutory matrix we have, A2=I. [ I being identity matrix of order 3].
So,
A2=I
or, A=A1 [ Since involutory matrix is always invertible]
or, A2=A12.

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