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Question

If A is involutary then|A|=1 or 1


A

True

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B

False

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Solution

The correct option is B

True


We know that for a matrix A to be called as involutery A2 should be equal to I

A2=I

So |A2|=|I||A|2=1(as determinant of identity matrix is 1).Also |A|2=|A|=|A|2(Refer to the of determinants which says that |AB|=|A||B|).Here A and B are same only)So |A|=1or1.


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