Let $\ast '$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a \ast ' b = H.C.F$ of a and b. Is the operation same as the operation $\ast$ defined in the table below? $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$

Question

$\begin{array}{1 1} \text{Yes, the two operations are the same} \\ \text{No, they are different} \end{array} $