So I have this matrix
A = $\begin{bmatrix}2 & 4\\1 & 1\end{bmatrix}$
I am tasked with finding all the elementary matrices such that Ek…E2E1A = I. Use this sequence to write both A and A-1 as products of elementary matrices/
I ended up getting four elementary matrices
E1 = $\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}$
E2 = $\begin{bmatrix}1 & 0\\-2 & 1\end{bmatrix}$
E3 = $\begin{bmatrix}1 & 0\\0 & 1/2\end{bmatrix}$
E4 = $\begin{bmatrix}1 & -1\\0 & 1\end{bmatrix}$
When I invert all the elementary matrices and multiply them it equals A but when I multiple All the elementary matrices by A I do not get the identity matrix
Best Answer
HINT Possibly you are multiplying in the wrong order. Remember in general $$(AB)^{-1} = B^{-1} A^{-1} \neq A^{-1} B^{-1}$$