1. The problem statement, all variables and given/known data Explain in your own words why the product of eigenvalues of any diagonalisable N × N matrix A must equal the determinant of A. 2. Relevant equations MT=M-1 3. The attempt at a solution So what I do know: the determinant measures the change in area of the unit square under the transformation (as the point (x,y) transforms to the point (X,Y)). And the eigenvectors describe the direction of the deformation of the matrix A - which are unchanged by the deformation. So my question is why does the product of the eigenvectors equal the determinant of the matrix A?