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

[sheldonrocks97]

Homework Statement

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

Homework Equations

None that I know about.

The Attempt at a Solution

I'm not sure where to start, I would like to know how to complete this problem.

 

[pasmith]

Homework Statement

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

Homework Equations

None that I know about.

The Attempt at a Solution

I'm not sure where to start, I would like to know how to complete this problem.

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

 

[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?

 

[AlephZero]

Find out about singular matrices.