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In my Linear Algebra Textbook one exercise is to find the matrix analogue of $$ \frac1a+\frac1b=\frac{a+b}{ab} $$ my immediate response was $$ A^{-1}+B^{-1}=A^{-1}(A+B)B^{-1} $$ is that a reasonable answer or do someone have better suggestions?

NOTE: $A$ and $B$ are assumed invertible $n\times n$ matrices.

String
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1 Answers1

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That is a good analogue, especially because it is true. I doubt there would be a neater one.

Joonas Ilmavirta
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    Thanks! I suppose the exercise aims at being aware of the non-commutativity of matrix multiplication ... I am not sure what the point would be apart from that. – String Aug 18 '14 at 12:53
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    @String, I assume the point is getting used to the multiplicative notation (using $A^{-1}B$ instead of $\frac BA$ so that order is never ambiguous) and being constantly aware that matrices need not commute. But that is a good point in early linear algebra. – Joonas Ilmavirta Aug 18 '14 at 12:57