A and B are n*n matrices. Check the true statements below. Please provide explanations. Thanks! -The determinants of A is the product of the diagonal entries in A. -If (lambda)+5 is a factor of the characteristic polynomial of A, then 5 is an eigenvalue of A. -(detA)(detB) = detAB -An elementary row operation on A does not change the determinant. -If(lambda-r)^k is a root of the characteristic polynomial of A, then r is an eigenvalue of A with algebraic multiplicity k. -If A is 3*3, with columns a1,a2,a3, then detA equals the volume of the parallelpiped determined by vectors a1,a2,a3. -If one multiple of one row of A is added to another row, the eigenvalues do not change. -detA(transpose) = (-1)detA