Here
$$
\begin{array}{l}
\mathrm{AA}^{\mathrm{T}}=\left(\begin{array}{cc}
2 & -1 \\
-7 & 4
\end{array}\right)\left(\begin{array}{cc}
2 & -7 \\
-1 & 4
\end{array}\right) \neq\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right) \\
\left(\mathrm{BB}^{\mathrm{T}}\right)_{11}=(4)^{2}+(1)^{2} \neq 1 \\
(\mathrm{AB})_{11}=8-7=1,(\mathrm{BA})_{11}=8-7=1
\end{array}
$$
$\therefore \mathrm{AB} \neq \mathrm{BA}$ may be not true.
$$
\begin{array}{l}
\text { Now, } \mathrm{AB}=\left(\begin{array}{cc}
2 & -1 \\
-7 & 4
\end{array}\right)\left(\begin{array}{ll}
4 & 1 \\
7 & 2
\end{array}\right) \\
=\left(\begin{array}{cc}
8-7 & 2-2 \\
-28+28 & -7+8
\end{array}\right)=\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right) \\
\therefore(\mathrm{AB})^{\mathrm{T}}=\left(\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right)
\end{array}
$$