True or False

Question

True or False   If A and B are matrices such that AB and BA are both defined, then A and B must be square matrices.

 

 

If you think the statement is true, then show that it is true. On the other hand, if you think the statement is false, then give an example that disproves the statement.

Answer 1

Hi LaToya,

 

Matrices have to have a certain kind of dimension in relation to one another in order for them to be "multiply-able"

 

 

3 by 2  & 2 by 5 for example are multiply-able  both the inner dimensions match 2-2

 

But the same matrices, when switched around, would give you 2 by 5 and 3 by 2.

 

The inner dimensions 2-5 do not match (i.e  are not equal).

 

As you can see, you can do the switching around only when all the dimensions are equal.

 

And the covers is also true - if they are multiply-able when switched around then they both are sqare matrices