If you pick a particular basis for then can be represented by a matrix , and can be represented by a matrix . We are told that , so . Therefore, is such a linear trasformation so that its corresponding matrix commutes with all other matrices. In order to complete your problem we need to show that is a scalar multiple of the identity matrix. Let . Define the matrix so that the entry is and everything else is . Notice that is always invertible. Thus, if commutes with every matrix it means . If the -entry in that matrix equation tells us that i.e. the matrix has all its diagnol entries equal. Now consider the matrix equation the -entry tells us . Thus, is a scalar of a diagnol matrix.