# Thread: Find elementary matrix E such that AB=EB

1. ## Find elementary matrix E such that AB=EB

Any help is appreciated!

2. Try:
-1 0
0 1

3. $

im(B)=span(\begin{bmatrix}-1 \\1 \end{bmatrix})~,~
AB-EB=0\rightarrow (A-E)B=0\rightarrow
\begin{bmatrix}-1 \\1 \end{bmatrix} \in ker(A-E)

$

If suppose $A-E= \begin{bmatrix}1&1 \\1&1 \end{bmatrix}
\rightarrow E=\begin{bmatrix}-1&0 \\-1&0 \end{bmatrix}

$

4. Originally Posted by math2009
$

im(B)=span(\begin{bmatrix}-1 \\1 \end{bmatrix})~,~
AB-EB=0\rightarrow (A-E)B=0\rightarrow
\begin{bmatrix}-1 \\1 \end{bmatrix} \in ker(A-E)

$

If suppose $A-E= \begin{bmatrix}1&1 \\1&1 \end{bmatrix}
\rightarrow E=\begin{bmatrix}-1&0 \\-1&0 \end{bmatrix}

$
That is NOT an elementary matrix.