[Python] Row Echelon form of matrix using python coding without using any inbuilt functions

I'm trying to write a code for the row Echelon form of \ matrix using Python without using any inbuilt functions. But I'm getting an error for last column.

A=[[1,2,3],[4,5,6],[7,8,9]]

j=0;k=0

print("Input matrix",A)


for i in range(3):

a=A
while j < 3:
A[j]=A[j]/a
j=j+1
j=1
b=A[j][k]
while k < 3:
if k < 3 and j < 3:
A[j][k]=A[j-1][k]*b-A[j][k]
k=k+1
j=1
k=1
print("output matrix",A)


output:

Input matrix [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

output matrix [[1.0, 2.0, 3.0], [0.0, 1.0, 2.0], [7, 0.888888, 1.0]]




the last row first element and second element should be zero.

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