# Matrix Products

1. Oct 17, 2012

### Bashyboy

1. The problem statement, all variables and given/known data
What do we know about the sizes of the matrices A and
B if both of the products AB and BA are defined?

2. Relevant equations

3. The attempt at a solution
I determined the sizes, of which were correct; but I was wondering if A and B would always be squares. Well, would they always be squares?

2. Oct 17, 2012

### clamtrox

Well, when is the product AB defined? How about BA?

3. Oct 17, 2012

### Staff: Mentor

Suppose A is m X n (m rows and n columns), and B is r X s. For AB to be defined, what relationship must there be between A's rows or columns and B's rows or columns? How many rows and columns will AB have?

For BA to be defined, what relationship must there be between B's rows or columns and A's rows or columns? How many rows and columns will BA have?

4. Oct 17, 2012

### Bashyboy

For AB to be defined, n = r. For BA to be defined, s = m. Right?

5. Oct 17, 2012

### Staff: Mentor

Right.

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