Question

Let $A$ and $B$ are square matrices of order $2,$ such that $|A|=6$ and $|B|=5.$ If the value of $|3A||4B|=\alpha ,$ then the value of $\frac{\alpha }{144}$ is

Answer 1

Given $|A|=6$ and $|B|=5$
$\Rightarrow |3A||4B|=3^2|A|\cdot 4^2|B|$
$(\therefore |KA|=K^n|A|,\text{where}n\text{is the order of}A)$
$\Rightarrow |3A||4B|=9\cdot 16\cdot |A|\cdot |B|$
$=9\cdot 16\cdot 6\cdot 5=\alpha$
$\alpha =144\cdot 30$
$\therefore \frac{\alpha }{144}=30$