TITLE: Matrix-version of $\frac1a+\frac1b=\frac{a+b}{ab}$?
QUESTION [10 upvotes]: 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.

REPLY [11 votes]: That is a good analogue, especially because it is true.
I doubt there would be a neater one.