There are Numerical recipes (For C) functions namely ludcmp() and lubksb() to invert the matrix. I used them for a simple 3x3 matrix. I got the inverse. Then I mulitiplied that inverse with the original matrix. As expected I got the identity matrix.
Now the same thing I tried for my 100x100 sparse matrix. I got the inverse. So to check, I multiplied this inverse by original matrix. But I did not get Identity matrix.
Please tell efficient and correct way to invert a sparse matrix?