# Finding nonzero matrices that result in AB=0

• Apr 11th 2011, 12:54 PM
DrZ
Finding nonzero matrices that result in AB=0
This question has confused me a bit.

Find nonzero 2x2 matrices A and B such that AB=0.

I've been just trying to find two 2x2 matrices who result in a 2x2 matrix with 0 at each position.

A =
1 1
1 1

B=

1 1
-1-1

so AB =
0 0
0 0

I think that is correct, but the question ased for AB=0, does that mean a matrix with 0 in all positions?
• Apr 11th 2011, 01:11 PM
TheChaz
Quote:

Originally Posted by DrZ
This question has confused me a bit.

Find nonzero 2x2 matrices A and B such that AB=0.

I've been just trying to find two 2x2 matrices who result in a 2x2 matrix with 0 at each position.

A =
1 1
1 1

B=

1 1
-1-1

so AB =
0 0
0 0

I think that is correct, but the question ased for AB=0, does that mean a matrix with 0 in all positions?

It DOES mean a matrix with zero in all positions!
1 0
0 0

and

0 1
0 0 ??
• Apr 11th 2011, 01:27 PM
emakarov
The OP's example also works.
• Apr 11th 2011, 01:32 PM
TheChaz
Quote:

Originally Posted by emakarov
The OP's example also works.

Of course. I guess it's worth mentioning that "0" in the context of a matrix product means the zero matrix.