Unit Matrix is Proper Orthogonal

Theorem
The unit matrix $\mathbf I_n$ of order $n$ is proper orthogonal.

Proof
By Unit Matrix is Orthogonal, $\mathbf I_n$ is an orthogonal matrix.

By Determinant of Unit Matrix, the determinant of $\mathbf I_n$ is equal to $1$.

The result follows by definition of proper orthogonal.