TITLE: What is the point of a $1\times 1$ matrix?
QUESTION [5 upvotes]: Surely a $1\times 1$ matrix can only 'produce' vectors with 1 entry, and can take as input also only one entry vectors.
So, is there any use for $1\times 1$ matrices?
Since to me they do the same like scalars, only worse.

REPLY [2 votes]: The point of a $n\times n$ (or $m\times n$)matrix is usually to generalize to $n$ dimensions what you already knew in $1$-dimension. And the point of the $1\times 1$ matrix is to give you back what you knew in $1$-dimension. So you won't need to prove something twice, once for 1-dimension and once for multiple dimensions (ಠ‿ಠ)