Matrix/2/Left inverse/Right inverse/Exercise

Let ${}M={\begin{pmatrix}a&b\\c&d\end{pmatrix}}$ and ${}A={\begin{pmatrix}x&y\\z&w\end{pmatrix}}$ be matrices over a field ${}K$ such that

${}A\circ M={\begin{pmatrix}1&0\\0&1\end{pmatrix}}\,$

holds. Show directly that

${}M\circ A={\begin{pmatrix}1&0\\0&1\end{pmatrix}}\,$

holds as well.

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