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Involutory Matrix

If A is invol...

Question

If A is involutary then $| A | = 1 o r - 1$

A

True

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B

False

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Solution

The correct option is A
True

We know that for a matrix A to be called as involutery $A^{2}$ should be equal to I

$A^{2} = I$

$S o | A \land 2 | = | I | {| A |}^{2} = 1 (a s d e t e r m i n a n t o f i d e n t i t y m a t r i x i s 1) . A l s o {| A |}^{2} = | A | = {| A |}^{2} (R e f e r t o t h e o f d e t e r m i n a n t s w h i c h s a y s t h a t | A B | = | A | | B |) . H e r e A a n d B a r e s a m e o n l y) S o | A | = 1 o r - 1.$

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