Question

If A=$\begin{bmatrix}1&2\\\4&2\end{bmatrix}$,then show that $\mid2A\mid=4\mid A\mid$

Answer 1

The given matrix is A=$\begin{bmatrix}1&2\\\4&2\end{bmatrix}$
therefore 2A=2 $\begin{bmatrix}1&2\\\4&2\end{bmatrix}$=$\begin{bmatrix}2&4\\\8&4\end{bmatrix}$
so LHS=$\mid 2 A\mid=\mid 2484 \mid$
=2x4-4x8=8-32=-24
Now IAI=$\mid \begin{matrix}1&2\\\4&2\end{matrix}\mid$=1x2-2x4=2-8=-6
therefore RHS=4IAI=4x(-6)=-24

So LHS=RHS