4. Consider the set G = {I, A, A2, A3, A4, A5}, where: 0 1 0 0 0 , A3 = 0 0 , A = 0 0 1 1 0 0 I = 0 0 0 1 0 , A 0 1 1 00 = 0 0 , A = 0 1 0 I A A A3 1 4 A5 0 0 1 0 , A5 = 00 00 0 Complete the multiplication table below for G with respect to matrix multiplication. In your table, please refer to the matrices as A, A2, and so on (i.e., do not write out the full matrices). I A A A3 A4 A5 1 (b) Determine whether G is a group with respect to matrix multiplication, and state the inverse of each invertible element. If needed, you may refer to your table above as an aid to justify any properties, but be specific with what exactly in the table you are drawing attention to. 0