
Have I got these properties of matrices correct?

Have I got these properties of matrices correct?
Your answers are correct, except that C is false. The right side is the inverse of $BA$, because $$(A^{-1}B^{-1})(BA)=A^{-1}(B^{-1}B)A=A^{-1}IA=A^{-1}A=I.$$ But must the inverse of $AB$ be the inverse of $BA$? See if you can find an explicit counterexample.