Question

If $A$ and $B$ are square matrices of order 3 such that $|A|=-1,|B|=3$, then the determinant of $3AB$ is equal to

• A. $-9$
• B. $-27$
• C. $-81$
• D. $81$

Answer 1

The correct option is C $-81$

We know that
$\left|AB\right|=\left|A\right|\left|B\right|$
Also for a square matrix of order 3
$\left|KA\right|=K^3\left|A\right|$because each element of the matrix A is multiplied by k and hence in this case we will have k${}^3$ common.
$\therefore \left|3AB\right|=3^3\left|A\right|\left|B\right|=$
$=27(-1)\left(3\right)=-81$