Question:
If $\left[\begin{array}{ll}a+b & 2 \\ 5 & b\end{array}\right]=\left[\begin{array}{ll}6 & 5 \\ 2 & 2\end{array}\right]$, then find $a$
Solution:
The corresponding elements of two equal matrices are equal.
$\Rightarrow\left[\begin{array}{cc}a+b & 2 \\ 5 & b\end{array}\right]=\left[\begin{array}{ll}6 & 5 \\ 2 & 2\end{array}\right]$
$\Rightarrow a+b=6$ ....(1)
$\therefore b=2$
Putting the value of $b$ in eq. (1)
$a+2=6$
$\Rightarrow a=6-2$
$\therefore a=4$