3.2.5. Consider the set G of nbyn matrices with entries in {0, 21:1} that have exactly one nonzero entry in each row and column. These are called signed permutation matrices. Show that G is a group, and that G is a semidirect product of Sn and the group of diagonal matrices with entries in {:l:l}. 5,, acts on the group of diagonal matrices by permutation of the diagonal entries. One nal example shows that direct products and semidirect products do not exhaust the ways in which a normal subgroup N and the quotient group G/ N can be t together to form a group G