Question

If $A^3=\left[\begin{array}{cc}-3& 0\\ 7& 9\end{array}\right]$, then $|A|$ is equal to

• A. $-3$
• B. $3$
• C. $-81$
• D. $7$

Answer 1

Answer: (A)

$-3$

$A^3=\left[\begin{array}{cc}-3& 0\\ 7& 9\end{array}\right]$

$|A^3|=-3\times 9-0=-27$

$\Rightarrow |A^3|=|A{|}^3=-27$

$\Rightarrow |A|=-3$

Hence, option A.