Question
$A=\left[\begin{array}{ll}5 & 4 \\ 1 & 3\end{array}\right], C_1 \leftrightarrow C_2 ; B=\left[\begin{array}{ll}3 & 1 \\ 4 & 5\end{array}\right], R_1 \leftrightarrow R_2$. What do you observe?
By $C _1 \leftrightarrow C _2$, we get,
$\begin{aligned}& A \sim\left[\begin{array}{ll}4 & 5 \\3 & 1\end{array}\right] \\& B=\left[\begin{array}{ll}3 & 1 \\4 & 5\end{array}\right]\end{aligned}$
By $R_1 \leftrightarrow R_2$, we get,
$B \sim\left[\begin{array}{ll}4 & 5 \\3 & 1\end{array}\right] \ldots(2)$
From (1) and (2), we observe that the new matrices are equal.
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