I'm trying to determine the exact complexity of finding an $n\times n$ matrix inverse of $A$.If it is known that the complexity of Gaussian elimination is $\frac{2}{3}n^3 + \frac{1}{2}n^2+O(n)$, then is it true that the complexity of finding $A^{-1}$ should be about twice same, since we are effectively doing two sets of Gaussian eliminations in parallel plus some row interchanges and multiplications?Please correct me if I'm wrong.
Complexity of matrix inverse via Gaussian elimination
time complexity;matrices;linear algebra