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The identity matrix is the matrix for which $a_{ij} = 1$ when $i = j$, and 0 everywhere else. For example, in three dimensions, \begin{align*}I =
\left[ \begin{array}{lll}
1 & 0 & 0
\\ 0 & 1 & 0
\\ 0 & 0 & 1
\end{array} \right]
\end{align*}