If matrix A is 3 x 3 and B is 4 x 3, how many multiplicities can be made?

Question

What matrix multiplication combinations are possible?

My book says that it is impossible but the only options are AB, BA, AA, BB and states (select all that apply.) I would say AA, and BB but not the other two. Any help understanding would be appreciated. 

 

Thank you

Answer 1

For non-square matricies to be multiplied, the number of columns of the first must be equal to the number of rows in the second.

 

₃A₃ x ₄B₃, no, 3 ≠ 4.

 

₄B₃ x ₃A₃, yes, 3 = 3

 

Check the others.