The link says it calculates the pseudo-inverse. The pseudo-inverse is a well known and useful concept, but it is NOT the same as the inverse.
The answer to the OP's questiion is "no".
No, if a matrix is invertible it is said to be non-singular which is the exact opposite of singular.
In other words a singular matrix has got a zero determinant and as such it's inverse cannot be obtained.A non singular matrix has got the determinant not equal to zero and in the due course it's inverse can be obtained hence the name invertible matrix.
@AlephZero and kaliro - Point conceeded.
@phymatter please accept my apologies if my post was misleading.