So, the question is indeed asking for what you just read. I have the following matrix for which I have to find the values of $k$ in order to make it not invertible. I have understood that the inverse of a matrix is the result of $[A | I]$, so since I have to solve in row echelon form in order to find its inverse, I got stuck when the time came to put it from row echelon to reduced row echelon form because I have $k$ in the lowest right-hand corner.
This is how the matrix looks like in row echelon form. The problem is that I don't know how to continue, even if I was to know how to get into reduced row echelon form, I wouldn't know how to find a number that would make the matrix not invertible. Am I supposed to give the value of k that would be anything but one? (because the matrix in the end has to be equal to the identity right?) Please, I would greatly appreciate your help.