&gt;Great. But don&#x27;t you then use the factorization to determine the inverse of A (LAPACK example: call dgetrf to get the factorization, then call dgetri to compute the inverse using the factorization)?<p>No.<p>&gt;How else would you solve Ax = b for x?<p>Call dgetrs instead of dgetri.<p>You use the factorisation directly (not the inverse) to get x from b.  This is done by calling dgetrf to get the factorisation, then calling dgetrs to get the solution.  You don&#x27;t need to call dgetri.<p>I&#x27;d do an example, but there are other replies to your comment that go through the mathematics.