Given a non-singular matrix $A$, is it possible to find $A^{-1}$ using Gaussian elimination, without LU and without Gauss–Jordan?
I know that I can use LU decomposition and then apply Gaussian elimination on $L$ and $U$. This would require :
Finding $L$ and $U$
Calculate $L*Y = e(i)$ , from here I'd get $Y$
Calculate $U*(current-column) = Y$ , from here I'd get each time the column
Or, I can use Gauss–Jordan method (without LU decomposition) where I put the $I$ matrix on the right of $A$, and then use the Gauss–Jordan elimination.
Both ways work great, but, is it possible to calculate the inverse of $A$ only with Gaussian elimination?
Regards