Question

If $A$ is an involuntary matrix then $|A|$ is equal to

• A. $\pm 2$
• B. $\pm 1$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

Answer: (B)

$\pm 1$

Given that $A$ is involuntary matrix

Involuntary matrix is a matrix that is equal to its own inverse

$\Rightarrow A=A^{-1}$

Apply det on both sides , we get

$\Rightarrow |A{|}^2=1$

$\Rightarrow |A|=\pm 1$

Therefore the correct option is $B$