Question

If $A=(\begin{array}{ccc}1& 2& 3\\ 2& 4& -5\\ 3& -5& 6\end{array})$, then verify that $(A^T{)}^T=A$.

Answer 1

$A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& -5\\ 3& -5& 6\end{array}\right]$

To proof : ${\left[A^T\right]}^T=A$

$\Rightarrow$ Now, $A^T=\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& -5\\ 3& -5& 6\end{array}\right]$

$\Rightarrow {\left[A^T\right]}^T=\left[\begin{array}{ccc}1& 2& 3\\ 2& 4& -5\\ 3& -5& 6\end{array}\right]=A$

Hence, proved.