College Algebra, Chapter 7, 7.2, Section 7.2, Problem 36

Find $x$ and $y$ if $\displaystyle 3 \left[ \begin{array}{cc}
x & y \\
y & x
\end{array} \right] = \left[ \begin{array}{cc}
6 & -9 \\
-9 & 6
\end{array} \right]$

Since the two matrices are equal, corresponding entries must be the same. So we must have $3x = 6$ and $3y = -9$. Then,


$
\begin{equation}
\begin{aligned}

x =& \frac{6}{3}
\qquad \text{Divide by } 3
\\
\\
x =& 2

\end{aligned}
\end{equation}
$


and


$
\begin{equation}
\begin{aligned}

y =& \frac{-9}{3}
\qquad \text{Divide by } 3
\\
\\
y =& -3

\end{aligned}
\end{equation}
$


Therefore,

$\displaystyle 3 \left[ \begin{array}{cc}
2 & -3 \\
-3 & 2
\end{array} \right] = \left[ \begin{array}{cc}
6 & -9 \\
-9 & 6
\end{array} \right]$