How useful are non-square matrices in maths or sciences? I know that a matrix will be either square or rectangular matrix. I know that square matrices are used to solve a system of linear equations. But what's the use of rectangular matrices, why do we study them? Are they used somewhere in Math or science? Please answer my questions.

Rectangular matrices are almost as usable as square matrices, just for different things. For instance, you might be interested in a linear map $\Bbb R^n \to \Bbb R^m$ where $n$ does not equal $m$. Then the map may be represented as a rectangular matrix.
Perhaps the most important everyday application is linear regression where you find the closest almost-solution to an overdetermined system of linear equations (say $900$ equations in $50$ unknowns, for instance).
