Answer
The determinant equals $1$.
Work Step by Step
An elementary row replacement matrix looks like the identity matrix, but with some entry $k\neq0$ either above or below the main diagonal. Hence, such a matrix will be either upper triangular or lower triangular, allowing us to apply Theorem 2. Since all the entries along the diagonal of the identity matrix are $1$, the determinant will be $1\times1\times\cdots\times1=1$.
