Have I got these properties of matrices correct?
Properties of matrices
3
$\begingroup$
matrices
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1$(AB)^{-1}=B^{-1}A^{-1}$ – 2012-03-04
1 Answers
0
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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0sorry i meant distributing the 3 – 2012-03-04