Let V be some vector space and S be a subset.
a. V=T(3,3) and S is the set of invertible linear transformations.
I know the V represents all linear transformations from R^3 -> R^3, and all linear transformations in S must be invertible, thus they must all be bijective. But I'm unsure how to go about this?
I know the three conditions that establish a subspace - S contains the 0 vector, S is closed under addition, and S is closed under scalar multiplication. Just not sure how to proceed.