Question

If $A=\left[\begin{array}{cc}1& 5\\ 6& 7\end{array}\right]$, then find $A+A^{\prime }$.

Answer 1

Given $A=\left[\begin{array}{cc}1& 5\\ 6& 7\end{array}\right]$

So transpose of $A$ is,

$A^{\prime }=\left[\begin{array}{cc}1& 6\\ 5& 7\end{array}\right]$, exchange rows and columns

Therefore,

$A+A^{\prime }=\left[\begin{array}{cc}1& 5\\ 6& 7\end{array}\right]+\left[\begin{array}{cc}1& 6\\ 5& 7\end{array}\right]=\left[\begin{array}{cc}1+1& 5+6\\ 6+5& 7+7\end{array}\right]=\left[\begin{array}{cc}2& 11\\ 11& 14\end{array}\right]$