I don't want to sound mean, but the simple fact that you forgot to divide by the matrix determinant for me is a great illustration of why using a library might

I don't want to sound mean, but the simple fact that you forgot to divide by the matrix determinant for me is a great illustration of why using a library might be a good option. I think for most of us can make this mistake, and reasoning in higher order (i.e. using a function from a tested library) helps avoiding this kind of error.