M22 is the vector space of 2 2 matrices. Let S22 denote the set of all

Question:

M22 is the vector space of 2 × 2 matrices. Let S22 denote the set of all 2 × 2 symmetric matrices. That is
S22 = {A ∈ M22 | At = A}
1. Show that S22 is a subspace of M22.
2. Exhibit a basis for S22 and prove that it has the required properties.
3. What is the dimension of S22?