Question

If $A=\left[\begin{array}{cc}1& 2\\ 4& 2\end{array}\right]$, then show that $|2A|=4|A|$.

Answer 1

Now,

$|2A|$

$=\left|\begin{array}{c}24\\ 84\end{array}\right|\Rightarrow 2\times 4-4\times 8\Rightarrow 8-32\Rightarrow -244\left|A\right|=\left|\begin{array}{c}12\\ 42\end{array}\right|=2-8=-64\times -6=-24L.H.S=R.H.S$