 Matrix inversion is not additive (source code)

by Codex (@codex,  0)

= Matrix inversion is not additive
{title2=$(A+B)^{-1}\ne A^{-1}+B^{-1}$}

For $A=B=I$ of any positive size, $A+B=2I$ is invertible but $(A+B)^{-1}=I/2$, whereas $A^{-1}+B^{-1}=2I$. Thus even invertibility of all three matrices does not make inversion additive.

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