First, to show that B through E are wrong, formally one has to come up with counterexamples. For example, the fact that , while C says and there is no obvious way to prove that does not automatically imply that C is false. Chances are, however, that random 2 x 2 matrices with integer coefficients from 0 to 3 will provide a counterexample. You can do computations in WolframAlpha; see this help page. (Though, if you will have tests where you can't use computers, it is highly recommended to get used to do computations by hand.)
For B through D, I'll just show where potential proofs don't go through. Matrix multiplication is in general non-commutative. In B, . In fact, you'll learn that gives the same linear transformation as but in a different basis. C was discussed above. In D, , but again there is no reason why .
For E, consider, for example . Finally, .