Question

谁能帮我解答下面英语线性代数题Let A n*n and Bn*n are such that AB is invert

Answer 1

forget the hint.prove:det(AB)=det(A)det(B)≠0,（AB is inversible) so det(A)≠0 and det(B)≠0 that means both A and B are invertible.anothern=rank(AB)≤rank(A)≤n n=rank(AB)≤rank(B)≤n so rank(A)=rank...