Originally Posted by

**anncar** Consider the set G of all 2×2 non-zero matrices of the

form (a b )

.......(b a + b)

where a, b belong to Z3, the set of congruence classes modulo 3.

(1) Find the number of elements in the set G.

(2) Prove that G is a group under matrix multiplication modulo 3.

(3) Complete the multiplication table for G.

(4) Is the group G isomorphic to the group of symmetries of a square?

(two groups are isomorphic if there exists a bijection

between them that preserves the group operations, in other words,

after an appropriate permutation and relabeling of the elements,

their multiplication tables are identical.