Since, undergrads are supposed to to their assignment themselves :-) , I will leave you with a hint here: Every symmetric real square matrix can be diagonalized i.e. If A is a n X n symmetric matrix then for an invertible matrix B, we have A = B^(-1) D B , where D is a diagonal matrix. Thus A is similar to D over R. You have to prove this for n = 2. Now , the hint: Find the Eigen vectors and Eigen values of A. Create a matrix containing those Eigen vectors as its columns (Call it B). Then ,u will have B A B^(-1) = D where D is a diagonal matrix whose diagonal elements are the Eigen values of A.