Question

If A is a diagonal matrix of order 3 $\times$ 3 is commutative with every square matrix of order 3 $\times$ 3 under multiplication and trace (A) = 12, then

• A. $\left|A\right|=64$
• B. $\left|A\right|=16$
• C. $\left|A\right|=12$
• D. $\left|A\right|=0$

Answer 1

The correct option is A $\left|A\right|=64$

A diagonal matrix is commutative with every square matrix if it is scalar matrix so every diagonal element is 4.
$\therefore \left|A\right|=64$.