how does the multiplication of a column matrix and its transpose equal to one another commutatively?

Question

In Sir Rohan Abeyaratne's (of MIT mechanical engineering) lecture notes "The Mechanics of Elastic Solids", on the seventeenth page in pdf and the third page on the paper, it is stated that for any $n\times1$ column matrix $\{x\}$ we should note that

$\{x\}^T\{ x\}$=$\{ x\}\{x\}^T $

I cannot understand how this equation holds. The left-hand side is a 1 by 1 matrix and the right-hand side is a n by n square matrix. How come these two equal to each other?

The url of said lecture notes is

http://web.mit.edu/abeyaratne/Volumes/RCA_Vol_1_Math_Apr2014.pdf

Answer 1

You are right, $\{x\}\{x\}^T$ is a $ n\times n $ matrix, not a $1\times 1$ one. Probably a typo. If you see it actually used somewhere in the book, feel free to ask for another clarification, but I doubt you will.

Answer 2

I sent an e-mail to Sir Rohan Abeyaratne regarding the equation and He wrote and answer and He established that this is an error and stated that the equation should be $\{x\}^T\{ x\}$ = $x_1^2$+.. I hereby thank him again.