Let R2x2 be the vector space of 2 x 2 real matrices. A basis for R2x2 is Let f : R2x2 -> R be a lincar transformation such that f(12) = 2 and f(AB) = f(BA) for any A, B C R2x2. Use the above basis to prove that f(A) = 01,1 + 02,2 for any matrix A C R2x2