# Computational efficiency using Gaussian elimination

Assume it took 2 seconds to solve an equation Ax=b for x (where A is a 3×3 matrix and b is a 3×1 matrix) using Gaussian elimination, how much longer would it take to:

a) use Gaussian elimination to find $A^{−1}$ and then find $x=A^{−1}\cdot b$

b) if A were a 30×30 matrix and b were a 30×1 matrix and I used Gaussian elimination to find x

c) if A were a 30×30 matrix and b were a 30×1 matrix and I used Gaussian elimination to find $A^{−1}$ and then find x from x=$A^{−1} \cdot b$

To get started, I know that I will need to use $\frac 23n^3$ where n is the number of operations. I know this article touches on it. But what exactly do i need to do. How many operations does it take to find $A^{-1}$ and then the operation $A^{-1}\cdot b$. How could i figure this out? thanks guys!

The efficiency of Gauss elimination is $\mathcal O (n^3)$, so it should take 2000 seconds to do a 30x30 matrix.