Step by step Gauss-Jordan reduction of a matrix : pivot

pivot takes three arguments : a matrix with n rows and p columns and two integers l and c such that 0 $\leq$ l < n, 0 $\leq$ c < p and A_{l, c} $\neq$ 0.
pivot(A,l,c) performs one step of the Gauss-Jordan method using A[l,c] as pivot and returns an equivalent matrix with zeros in the column c of A (except at row l).
Input :

pivot([[1,2],[3,4],[5,6]],1,1)

Output :

[[-2,0],[3,4],[2,0]]

Input :

pivot([[1,2],[3,4],[5,6]],0,1)

Output :

[[1,2],[2,0],[4,0]]