Question about Determinants and invertibility
This is kind of a broad question but I'm looking for kind of a thorough answer. Suppose you computed det(A*transpse(A)) and det(transpose(A)*A) for 10 random 5X6 matrices and 10 random 7X6 matrices. What happens? Can I generalize anything about determinants from this? Does this say anything about Invertibility? I've been finding as I do some calculations with the random matrices that det(A*transpse(A)) and det(transpose(A)*A) seem to equal 0. I'm not sure what this means, am I wrong here? Can this be explained along with the rest of the question?