Question

If A is involutory matrix and I is unit matrix of same order, then $(I-A)(I+A)$ is:

• A. zero matrix
• B. A
• C. $I$
• D. 2A

Answer 1

Answer: (A)

If $A$ in involutory matrix, then $A^2=I$
Since, $A$ is involutory matrix.
$\therefore A^2=I\dots ..(i)$
Now, $(I-A)(I+A)$
$=I^2-A^2$
$=I-I[$ from (i) ]
$=0$