Thank you for reporting, we will resolve it shortly
Q.
if $A= \begin{pmatrix}2&-1\\ -7&4\end{pmatrix}$ and $B=\begin{pmatrix}4&1\\ 7&2\end{pmatrix}$ then which statement is true ?
Matrices
Solution:
Here $AA^{T}=\begin{pmatrix}2&-1\\ -7&4\end{pmatrix}\begin{pmatrix}2&-7\\ -1&4\end{pmatrix}\ne\begin{pmatrix}1&0\\ 0&1\end{pmatrix}$
$\left(BB^{T}\right)_{11}=\left(d\right)^{2}+\left(a\right)^{2}\ne1$
$\therefore AB\ne BA$ may be not true
Now $AB \begin{pmatrix}2&-1\\ -7&4\end{pmatrix}\begin{pmatrix}4&1\\ 7&2\end{pmatrix}$
$=\begin{pmatrix}8-7&2-2\\ -28+28&-7+8\end{pmatrix}=\begin{pmatrix}1&0\\ 0&1\end{pmatrix}\,; \left(AB\right)^{T}=\begin{pmatrix}1&0\\ 0&1\end{pmatrix}=I$