Question

A really simple question, I was annoyed at myself that I have to ask it, but here I am. We have the following equation:

ABC=DEC

Here all letters stand for matrices. We can conclude that:

AB=DE

Regardless of the dimensions of the matrices. Correct?

Answer 1

i dont believe that you can just cancel out the C

Matrix rules dont allow this

Answer 2

Can you multiply matrices regardless of their dimension?

Answer 3

i dont think so

Answer 4

check on wiki

Answer 5

Yeah, sorry, I should have clarified that the expressions on each side are valid. That is, the dimensions of A, B, C, D, and E are appropriate for the multiplication.

Under what circumstances would ABC=DEC be true but not AB=DE?

Answer 6

How about C being the zero matrix?

Answer 7

Okay, I knew that :) But what if it's not the zero matrix?

Answer 8

I mean, I know it from the problem that none of them are the zero matrix.

Answer 9

i think it can only be true for the identity matrix no exceptions

Answer 10

could you explain? or could you give an example where C is not the identity matrix and it won't work?

Answer 11

Do some reading at this link:

http://science.kennesaw.edu/~plaval/math3260/matopprop.pdf

Answer 12

>>>could you give an example


http://thejuniverse.org/PUBLIC/LinearAlgebra/LOLA/matCalc/mult.html

Answer 13

Thanks for the reply Directrix. I think I get it now. The equality in my OP holds iff C is a square non-singular matrix OR CC' is non-singular (in case C is a rectangular matrix).