Let A,B, C be nxn real matrices

Let A, B, C be nxxn real matrices that are pairwise commutative and ABC is a null matrix. Show that det(A + B + C) det (A^3+ B^3 + C^3) geq0,

Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB and D^(T)=ABC for the matrix M=ABCD then find M^(3) ?

Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB and D^(T)=ABC for the matrix M=ABCD then find M^(3) ?

Let A,B and C be nxxn matrices. Which one of the following is a correct statement?

Let A,B and C be n xx n matrices.Which one of the following is a correct statement?

Let A,B and C be square matrices of order 3xx3 with real elements. If A is invertible and (A-B)C=BA^(-1), then

Let A,B and C be square matrices of order 3xx3 with real elements. If A is invertible and (A-B)C=BA^(-1), then

Let A,B and C be square matrices of order 3xx3 with real elements. If A is invertible and (A-B)C=BA^(-1), then

Let A; B; C be square matrices of the same order n. If A is a non singular matrix; then AB = AC then B = C