# Nonzero Matrcies A; B; C such that AC = BC and A does not equal B?

1. Feb 13, 2014

### sheldonrocks97

1. The problem statement, all variables and given/known data

Find nonzero matrices A; B; C such that AC = BC
and A does not equal B

2. Relevant equations

3. The attempt at a solution

I'm not sure where to start, I would like to know how to complete this problem.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 13, 2014

### pasmith

The simplest non-zero matrices are
$$\begin{pmatrix} 1 & 0 \\ 0 & 0 \end{pmatrix},\quad \begin{pmatrix} 0 & 1 \\ 0 & 0 \end{pmatrix},\quad \begin{pmatrix} 0 & 0 \\ 1 & 0 \end{pmatrix},\quad \begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}$$
Play around.

3. Feb 13, 2014

### kduna

If AC = BC, then AC - BC = 0. I.e. (A-B)C = 0.

Can you find two non-zero matrices that multiply to zero?

4. Feb 13, 2014