Question

Let $A$ and $B$ be two square matrices of order $3$ each and $|A|=2$ and $|B|=3$. Then find $|3AB|$.

Answer 1

Given, $A$ and $B$ be two square matrices of order $3$ each and

$|A|=2$ and $|B|=3$.

Now

$|3AB|$

$=3^3|AB|$ [ Since $A$ and $B$ are two square matrix of order $3$]

$=27\times |A|\times |B|$ [ Since $|AB|=|A|\times |B|$]

$=27\times 2\times 3$

$=162$.