Please help me to answer the question below in detail. I really don't understand it. Thank you so much, and have a great day!

Let V = M2x2 (R). (a) Define an inner product on V. Show that it satisfies all properties of inner products. (b) Find the length of C d 2c 2d (c) Show that the set of all diagonal 2x2 matrices is a subspace of V. Call this S. (d) Find a basis for S (prove it is a basis), and then find dim(S). (e) Find the orthogonal complement of S. (f) Project A = C C onto S. Interpret your result. (Is A diagonalizable?) -C -C