Consider a binary operation $*$ on the set $\{1, 2, 3, 4, 5\}$ given by the following multiplication table. Compute $(2 \,^* \,3) \,^* \,(4 \,^* \,5)$.
(Hint: use the following table)

$^*$	$1$	$2$	$3$	$4$	$5$
$1$	$1$	$1$	$1$	$1$	$1$
$2$	$1$	$2$	$2$	$2$	$2$
$3$	$1$	$2$	$3$	$3$	$3$
$4$	$1$	$2$	$3$	$4$	$4$
$5$	$1$	$2$	$3$	$4$	$5$

(B) From the given table:
$1$. Find the value of $(2 \,^* \,3)$. Looking at the row for $2$ and column for $3$,we get $(2 \,^* \,3) = 2$.
$2$. Find the value of $(4 \,^* \,5)$. Looking at the row for $4$ and column for $5$,we get $(4 \,^* \,5) = 4$.
$3$. Now,compute the final expression: $(2 \,^* \,3) \,^* \,(4 \,^* \,5) = 2 \,^* \,4$.
$4$. Looking at the row for $2$ and column for $4$ in the table,we get $2 \,^* \,4 = 2$.
Thus,the final result is $2$.