How to get Smith normal form of a matrix

Question

I have the following matrix

$$m=\left( \begin{array}{cccc} 0 & -1 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & -1 & 0 \\ \end{array} \right)$$

How does one compute the Smith normal form of this matrix?

Answer 1

A series of row swappings yields \begin{bmatrix} 1&0&0&1\\0&-1&1&0\\0&0&-1&0 \\0&0&0&1 \end{bmatrix}