For all $\alpha$ in $\mathbb{R}$ and for all distinct integers $i$ and $j$ between 1 and $n$, describe the effect on a square matrix $M$ of size $n$ of left multiplication by $I_n + \alpha E_{ij}$. Same question for right multiplication.
For all $\alpha$ in $\mathbb{R}$ and for all distinct integers $i$ and $j$ between 1 and $n$, describe the effect on a square matrix $M$ of size $n$ of left multiplication by $I_n + \alpha E_{ij}$. Same question for right multiplication.