Reference no: EM132230354

Question - Let G be the set of 3 x 3 matrices whose entries come from the set {0, 1, -1} and such that every matrix in G has exactly one nonzero entry in each row and each column. You may assume G is a group under the operation of matrix multiplication. (I recommend taking a couple of minutes to privately write down a couple of examples of elements in G and taking their matrix products to convince yourself that G is a group!).

(a) Write down an isomorphism φ between S₃ and a subgroup H ≤ G so that φ(e) is the identity matrix and φ sends

(12)|→ A

(13)|→ B

(23)|→ C

That is, write down φ((123)) and φ((132)). You do not have to verify that this is an isomorphism for this exam (but you should verify for yourself that it is in order to ensure you do the rest of this question correctly).