4 Let \(S\) be the set \(\{ 16,36,56,76,96 \}\) and \(\times _ { H }\) the operation of multiplication modulo 100 .
- Given that \(a\) and \(b\) are odd positive integers, show that \(( 10 a + 6 ) ( 10 b + 6 )\) can also be written in the form \(10 n + 6\) for some odd positive integer \(n\).
- Construct the Cayley table for \(\left( S , \times _ { H } \right)\)
- Show that \(\left( S , \times _ { H } \right)\) is a group.
[0pt]
[You may use the result that \(\times _ { H }\) is associative on \(S\).] - Write down all generators of \(\left( S , \times _ { H } \right)\).