i have 2 questions im finding hard to try and answer.

Let T1 : U -> V and T2 : V -> W be linear maps.

Show that the map T2 T1 : U ->W is linear.

and

A matrix which satisfies A^T = -A is called skew-symmetric. Show that if A is an n*n skew-symmetric matrix where n is an odd integer, then A has no inverse. (Hint: use the definition A^T = -A to find det A, ) but be careful!