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

True

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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

$A^{2} = I$

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

Suggest Corrections

Similar questions

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

$A = [\begin{matrix} 0 & 1 1 & 0 \end{matrix}] is an involutary matrix.$

$I f A \times A i . e ., A^{2} = I T h e n A i s s a i d t o b e i n v o l u t a r y m a t r i x$

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