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The number of 2x2 matrices X satisfying ...

The number of `2x2` matrices `X` satisfying the matrix equation `X^2=I(Ii s2x2u n i tm a t r i x)` is 1 (b) 2 (c) 3 (d) infinite

A

0

B

1

C

2

D

more then 3

Text Solution

Verified by Experts

The correct Answer is:
D
`because X^(2) = I rArr (X^(-1) X) X=X^(-1)I`
`rArr Ix = X^(-1)`
`rArr X = X^(-1)`
which is self invertible involutory matrix.
There are many such matrices which are inverse of their own.
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