6 (10 pts) Are the following groups? Say YES or NO. If YES, no justification required. If NO, give one reason why not (justifying your answer). (Try to check the properties mentally. There is little to write down. ) (a) integers under subtraction No (b) set of 2 x 2 matrices with integer entries having determinant equal to 0 under matrix addition (c) {2m . 5" | m, n E Z } under multiplication yes (d) the set of all permutations in S, which map 1 to 1 (that is, the set of all o E Sn such that o(1) = 1) yes