If A is involutary matrix, then which of the following is/are correct?

I + A is idempotent

No worries! We‘ve got your back. Try BYJU‘S free classes today!

I – A is idempotent

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(I + A)(I – A) is singular

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{I + A}{3}

is idempotent

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C (I + A)(I – A) is singular
$A^{2} = I$
$(I + A) (I - A) = I - A^{2} + I - I = O$

Suggest Corrections

Similar questions

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

A

A = ⎡ ⎢ ⎣ \begin{matrix} 0 & 1 & - 1 4 & - 3 & 4 3 & - 3 & 4 \end{matrix} ⎤ ⎥ ⎦

A / 2

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

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

Join BYJU'S Learning Program