Let $A$ be a $2$ x $2$ matrix with real entries and $det(A)$ is equal to $d$ which is non-zero. It is given that $det(A +d(adjA))=0$ where $adj$ stands for the adjoint of the matrix. We have to find the value of $det(A-d(adjA))$.
My approach was to assume a matrix with 4 real entries and then apply the given conditions. It did yield the required answer, but I think there may be a better method to do this. Any help would be appreciated. Thanks.