As inversion involves steps that use the determinant of the matrix, it's better to develop an algorithm that evaluates the determinant of the matrix faster than the conventional recursive way. I think extending the rule of Sarrus does the trick. So far we have used rule of sarrus as a light weight formula for evaluating determinants of 2x2 and 3x3 matrices. But extending it in the following way makes it applicable for higher order matrices too. And this algorithm has a time complexity O(2*n^2) for nxn matrices. // a is a n x n matrix Det_a=0 Sum1=0 Sum2=0 For count=0 to n-1 do For i=1 to n do J=i+count Val=(j>n)?n:0 j-=val product*=a[i][j] sum1+=product For count=0 to n-1 do For i=1 to n do J=n-count-(i+1) Val=(j<1)?n:0 J+=val product*=a[i][j] sum2+=product det_a=sum1-sum2 return det_a I want to use this algorithm in my GSoC project to evaluate determinants, and based on this implementation I'll develop algorithms for inversion and decomposition. But I think if we can make some changes to this algorithm, this may run faster. As you can see, this thing traverses the matrix twice. If we can achieve the goal in only one traversal calculating sum1 and sum2 simultaneously, then it'd be a bit faster, but here I lack ideas. So please provide me with some help in this regard. ~Ganesh Prasad