please answer part b. Thank you.

5. Consider the vector space V of 3 x 3 real symmetric matrices. (a) (2 points) Show that (S, T) = tr(ST) is an inner product on V. Hint tr denotes the trace of a matrix. (b) (2 points) Consider the matrices 0 SI = 1 O and S2 0 0 Find a matrix orthogonal to both Si and S2. (c) (2 points) Find an orthonormal basis for V using the matrices from above. (d) (2 points) Consider the matrix T= Find the orthogonal projection of T on the span of { S1, S2}