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Have I got these properties of matrices correct?

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    $(AB)^{-1}=B^{-1}A^{-1}$2012-03-04

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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.

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    sorry i meant distributing the 32012-03-04