Let $f$ be a permutation on the set $\lbrace 1, 2, 3, 4, 5, 6, 7 \rbrace$, defined as follows

$$f = ( 3\,1\,6 ) ( 1\,4\,5 )$$
(a) Write $f$ as a product of transpositions (not necessarily disjoint), separated by commas (e.g. $( 1, 2 ), ( 2, 3 ), \ldots$ ).

$f =$

(b) Write $f^{-1}$ as a product of transpositions in the same way.

$f^{-1} =$

Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x)) so $(1,3)(1,2)=(1,2,3)$ not $(1,3,2)$.