Question:
If $A=\left[\begin{array}{ll}5 & x \\ y & 0\end{array}\right]$ and $A=A^{T}$, then
(a) $x=0, y=5$
(b) $x+y=5$
(c) $x=y$
(d) none of these
Solution:
(c) $x=y$
Here,
$A=\left[\begin{array}{ll}5 & x \\ y & 0\end{array}\right]$
$A^{T}=\left[\begin{array}{ll}5 & y \\ x & 0\end{array}\right]$
Now,
$A=A^{T}$
The corresponding elements of two equal matrices are equal.
$\therefore\left[\begin{array}{ll}5 & x \\ y & 0\end{array}\right]=\left[\begin{array}{ll}5 & y \\ x & 0\end{array}\right]$
$\Rightarrow x=y$
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