- #1
simmonj7
- 66
- 0
1. Homework Statement
State whether true or false:
If A and B are singular matrices, then AB is also singular.
3. The Attempt at a Solution
I know that according to the Lemma, if A or B is a singular matrix, then its product AB is also singular. However, it doesn't speak to what happens if two both A and B are singular. I have tried examples using a bunch of singular matrices which I made, and all turned out to be singular. However, I can't get rid of this gut feeling that maybe there is an exception to this situation which I just can't put my finger.
State whether true or false:
If A and B are singular matrices, then AB is also singular.
3. The Attempt at a Solution
I know that according to the Lemma, if A or B is a singular matrix, then its product AB is also singular. However, it doesn't speak to what happens if two both A and B are singular. I have tried examples using a bunch of singular matrices which I made, and all turned out to be singular. However, I can't get rid of this gut feeling that maybe there is an exception to this situation which I just can't put my finger.