Question

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

Answer 1

If $A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ $\therefore A^{\prime }=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]$
Now $A^{\prime }A=\left[\begin{array}{cc}1& 3\\ 2& 4\end{array}\right]\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$
$=\left[\begin{array}{cc}1\times 1+3\times 3& 1\times 2+3\times 4\\ 2\times 1+4\times 3& 2\times 2+4\times 4\end{array}\right]$
$=\left[\begin{array}{cc}1+9& 2+12\\ 2+12& 4+16\end{array}\right]=\left[\begin{array}{cc}10& 14\\ 14& 20\end{array}\right]$