The collection Mn of n-by-n matrices is a vector space in the usual way: You can add matrices component-wise and multiply all their entries by scalars. Really, it is just a repackaging of R n 2 . Consider the linear map S : Mn → Mn given by S(A) = (A−At )/2, where t is the transpose. (a) (2 points) Apply S to a 2-by-2 matrix of your choice (don’t pick a trivial matrix, like the identity or the zero matrix).