Identity Matrix is Permutation Matrix

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Theorem

An identity matrix is an example of a permutation matrix.


Proof

An identity matrix, by definition, has instances of $1$ on the main diagonal and $0$ elsewhere.

Each diagonal element is by definition on one row and one column of the matrix.

Also by definition, each diagonal element is on a different row and column from each other diagonal element.

The result follows by definition of permutation matrix.

$\blacksquare$


Sources