We partition the identity matrix into columns as
\begin{equation*} I= (e_1 | e_2 | \cdots | e_n). \end{equation*}That is,
\begin{equation*} e_1 = \begin{pmatrix}1 \\ 0 \\ \vdots \\ 0 \\ 0\end{pmatrix} \quad e_2 = \begin{pmatrix}0 \\ 1 \\ \vdots \\ 0 \\ 0 \end{pmatrix} \quad \dots \quad e_n = \begin{pmatrix}0 \\ 0 \\ \vdots \\ 0 \\ 1 \end{pmatrix} \end{equation*} in-context