Question 13
Show that if $n \geq 2$ is an integer, then there exist invertible matrices $A_{1}, A_{2}, \ldots, A_{n} \in \mathcal{M}_{2}(\mathbb{R})$, with non-zero entries, such that $A_{1}^{-1}+A_{2}^{-1}+\ldots+A_{n}^{-1}=\left(A_{1}+A_{2}+\ldots+A_{n}\right)^{-1}$.