1. The problem statement, all variables and given/known data Two square matrices A and B of the same size do not commute.Prove that AB and BA has the same set of eigenvalues. I did in the following way:Please check if I am correct. Consider: det(AB-yI)*det(A) where y represents eigenvalues and I represents unit matrix =det[(AB-yI)A] =det[(AB)A-(yI)A] =det[A(BA)-A(yI)] =det(A)*det(BA-yI) det(A) is not equal to zero,in general. So,if det(AB-yI)=0,det(BA-yI)=0 also. hence, conclusion.