Matrix/Standard columns and rows/Exercise

Let ${}M$ be a ${}m\times n$- matrix. Show that the matrix product ${}Me_{j}$ of ${}M$ with the ${}j$-th standard vector (regarded as column vector), is the ${}j$-th column of ${}M$. What is ${}e_{i}M$, where ${}e_{i}$ is the ${}i$-th standard vector

(regarded as a row vector)?

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