Question 5
Prove that for every integer $n \ge 2$ one can find matrices $A_1, A_2, \dots, A_n \in \mathcal{M}_2(\mathbb{R})$, having non-zero entries, such that
$$
A_1^{-1} + A_2^{-1} + \dots + A_n^{-1} = (A_1 + A_2 + \dots + A_n)^{-1}.
$$
$$
A_1^{-1} + A_2^{-1} + \dots + A_n^{-1} = (A_1 + A_2 + \dots + A_n)^{-1}.
$$