If A= [ cc 5 & -3 4 & -3 -2 & 1 ], prove that (A^ )^ =A. - Vidyadip

Question

If $A=\left[\begin{array}{cc}5 & -3 \\ 4 & -3 \\ -2 & 1\end{array}\right]$, prove that $\left(A^{\top}\right)^{\top}=A$.

✓

Answer

$
\begin{array}{r}
A=\left[\begin{array}{rr}
5 & -3 \\
4 & -3 \\
-2 & 1
\end{array}\right] \\
\therefore A^{ T }=\left[\begin{array}{rrr}
5 & 4 & -2 \\
-3 & -3 & 1
\end{array}\right]
\end{array}
$
$
\therefore\left( A ^{ T }\right)^{ T }=\left(\begin{array}{rr}
5 & -3 \\
4 & -3 \\
-2 & 1
\end{array}\right)= A \text {. }
$

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