hi. i have recently become very interested in the idea of the nth roots of unity. i have discovered how to calculate them (using eigenvalues), and i find it very fascinating that there are not n many nth roots of unity(unlike scalars). aparently in the case where the matrix is 2x2, there are n^2 roots of unity my questions: given a size=k matrix, find the nth roots of unity. how many roots of unity are there? i want a general formula. is it n^k? What is the geometrical interperetation of the nth roots of unity of a matrix? the determinants of the nth roots are equal(analogous to the fact that the nth roots of unity of a scalar are points on a circle), but what about the placement of the vectors that compose the matrix? in other words, what is analogous to the fact that the roots of unity of a scalar form a regular polygon?