I am studying matrices and I have the next doubt:
Let's say we are in the 2-d world... A given matrix has 2 columns, so it is 2x2.
I interpret every column of the matrix as a point/vector, The same way 3blue1brown does it here https://youtu.be/kYB8IZa5AuE?list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B&t=389
If I have: \begin{bmatrix}2&0\\0&2\end{bmatrix}
It's inverse is:
\begin{bmatrix}1/2&0\\0&1/2\end{bmatrix}
This visually is just the points: (2,0), (0,2) and it's inverse are points (1/2, 0) , (0, 1/2), if I draw the vectors as arrows like 3blue1brown, the inverse doesn't follow in an intuitive way, why is this?
The inverse doesn't make any sense to me... Visually the inverse is just a 'shorter' version of the original one...