Please forgive my ignorance.
I am busy with a first year course in elementary linear algebra and there are some concepts I do not grasp. Particularly, questions regarding matrix invertibility.
For example, given that
$A^n = 0$ where $n \geq 1$
show that $A$ is not invertible, if $A$ was a matrix.
Now, from what I have learned from web searches is that a when a matrix is equal to $0$, it is call a nilpotent matrix. The problem is that this (including eigenvalues) are not covered in this course, so I am unsure of how to prove the above. Note that the question also doesn't mention $A$ being a square matrix, so I am unsure if even is a nilpotent matrix.
Any small hint to point me in the right direction will be appreciated.