This problem is #6 from pg. 83 of Hoffman & Kunze Linear algebra. A thorough explanation of the problem would be greatly appreciated.
by way of example, consider T: R^3 --> R^2 to be T(a, b, c) = (a, b) and
U : R^2 --> R^3 defined by U(a, b) = (a, b, 0)
then UT is defined by UT(a, b, c) = (a, b, 0) which is not invertible (it's the projection onto the first two ...
Not-Invertible Linear Transformations are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.