Question:
If $\left[\begin{array}{cc}a+4 & 3 b \\ 8 & -6\end{array}\right]=\left[\begin{array}{cc}2 a+2 & b+2 \\ 8 & a-8 b\end{array}\right]$, write the value of $a-2 b$.
Solution:
$\left[\begin{array}{cc}a+4 & 3 b \\ 8 & -6\end{array}\right]=\left[\begin{array}{cc}2 a+2 & b+2 \\ 8 & a-8 b\end{array}\right]$
Corresponding elements of equal matrices are equal.
$\therefore a+4=2 a+2 \quad$ and $\quad 3 b=b+2$
$\Rightarrow 4-2=2 a-a \quad$ and $\quad 3 b-b=2$
$\Rightarrow a=2 \quad$ and $\quad 2 b=2$
$\Rightarrow a=2 \quad$ and $\quad b=1$
$\therefore a-2 b=2-2=0$