Let A be a 4 x 4 matrix.
a) If the eigenvalues of A are 1,-2,3,-3, is it possible to determine det(A)? Why or why not?
b) What if the eigenvalues are -1,1,2?
c) What if the eigenvalues are -1,0,1?
I remember reading somewhere that the det(A) is equal to the product of all the eigenvalues of A but why is that so? If what I just said is true, wouldn't there be lack of information to calculate the determinant for parts b and c?