# Thread: Matrix equation

1. ## Matrix equation

A is a 2x2 matrix, if $\displaystyle A^{2}=0$, then the matrix A may not be a zero matrix, right?

Now if I have $\displaystyle AB=0$, then can I conclude that either $\displaystyle A=0$ or $\displaystyle B=0$?
A and B can both be non-zero also, right?

So then can I say that $\displaystyle AB=0$ implies $\displaystyle A=0$ or $\displaystyle B=0$ is not true in general? But when is it true, when is it not true?

Thank you!!

2. Originally Posted by acc100jt
A is a 2x2 matrix, if $\displaystyle A^{2}=0$, then the matrix A may not be a zero matrix, right?

Now if I have $\displaystyle AB=0$, then can I conclude that either $\displaystyle A=0$ or $\displaystyle B=0$?
A and B can both be non-zero also, right?

So then can I say that $\displaystyle AB=0$ implies $\displaystyle A=0$ or $\displaystyle B=0$ is not true in general? But when is it true, when is it not true?

Thank you!!
Yes:

For the first:

0 1
0 0

second:
A=
0 0
0 1

B=
0 1
0 0