I have a matrix below and I want to find $k$ such that this matrix becomes isomorphism. What should I do exactly? We are not allowed to use determinant! should we find $k$ such that this matrix is not invertible and if so how?
$$A=\left(\begin{array}{r;r;r;r} -1 & 0 & 1 & 0\\0 & 2-k & 0 & 3\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 4-k \end{array}\right)$$