Question

If $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right],$ find $|2A|$.

Answer 1

Given that $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

We have to find the determinant of matrix $2A$

We have $2A=2\times \left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]=\left[\begin{array}{cc}2& 4\\ 6& 8\end{array}\right]$

Therefore the value of $|2A|=\left|\begin{array}{cc}2& 4\\ 6& 8\end{array}\right|=2\times 8-6\times 4=16-24=-8$

Hence, $|2A|=-8$.