Easiest way to perform modular matrix inversion with Python?

Question

I'd like to take the modular inverse of a matrix like [[1,2],[3,4]] mod 7 in Python. I've looked at numpy (which does matrix inversion but not modular matrix inversion) and I saw a few number theory packages online, but nothing that seems to do this relatively common procedure (at least, it seems relatively common to me).

By the way, the inverse of the above matrix is [[5,1],[5,3]] (mod 7). I'd like Python to do it for me though.

Answer 1

Okay...for those who care, I solved my own problem. It took me a while, but I think this works. It's probably not the most elegant, and should include some more error handling, but it works:

import numpy import math from numpy import matrix from numpy import linalg  def modMatInv(A,p):       # Finds the inverse of matrix A mod p   n=len(A)   A=matrix(A)   adj=numpy.zeros(shape=(n,n))   for i in range(0,n):     for j in range(0,n):       adj[i][j]=((-1)**(i+j)*int(round(linalg.det(minor(A,j,i)))))%p   return (modInv(int(round(linalg.det(A))),p)*adj)%p  def modInv(a,p):          # Finds the inverse of a mod p, if it exists   for i in range(1,p):     if (i*a)%p==1:       return i   raise ValueError(str(a)+" has no inverse mod "+str(p))  def minor(A,i,j):    # Return matrix A with the ith row and jth column deleted   A=numpy.array(A)   minor=numpy.zeros(shape=(len(A)-1,len(A)-1))   p=0   for s in range(0,len(minor)):     if p==i:       p=p+1     q=0     for t in range(0,len(minor)):       if q==j:         q=q+1       minor[s][t]=A[p][q]       q=q+1     p=p+1   return minor