Edit: Sorry, I completely messed up my original answer here. A better version:

Let's say we are in a setting where we only work with integers. A matrix is invertible iff its determinant is invertible in the underlying ring. The only invertible elements in Z are -1 and 1.

So, the code is also incorrect in the integer setting. Here, we should not check for 0, but for -1 or 1.