In matrix algebra, if A is a horizontal matrix and B is a vertical matrix, what's the main difference between the products AB and BA?

Question

zepdrix · Answer

Mmm I don't remember the matrix stuff very well ;c
So if A is horizontal, like $\large\rm A_{1\times m}$ and B is vertical, like $\large\rm B_{n\times1}$

Then $\large\rm BA=C_{1\times1}$

Where as $\large\rm AB$ is only defined if the number of columns in A are the same as the number of rows in B.

Did I get it? +_+ maybe? lil bit?

zepdrix · Answer

BA = an nxm matrix* blah

nuttyliaczar · Answer

Oh right I should have defined n and m first woops my bad

nuttyliaczar · Answer

Assume they are equal (n=m)

zepdrix · Answer

Then BA = an MxM matrix,
whereas AB = a 1x1 matrix

? :o
something like that? lil bit?

nuttyliaczar · Answer

Yep that's right! You don't need to say that AB is a 1x1 but technically that is right so ^^

nuttyliaczar · Answer

I was looking for a more broad answer, like AB gives a scalar and BA gives another matrix

zepdrix · Answer

Ooo clever >.< I see

nuttyliaczar · Answer

Honorary Professor of Mathematics + 1

zepdrix · Answer

୧ʕ•̀ᴥ•́ʔ୨

nuttyliaczar · Answer

Looks like a gopher. I've never seen a gopher before but if I had to picture one then that's it

zepdrix · Answer

It's a bear :3 lol

nuttyliaczar · Answer

Yes we shall go with that. Bear it is, by unanimous vote