Let `A ,B` be two matrices such that they commute, then for any positive integer `n ,` `A B^n=B^n A` `(A B)^n A^n B^n` only (i) and (ii) correct both (i) and (ii) correct only (ii) is correct none of (i) and (ii) is correct

Let A,B be two matrices such that they commute.Show that for any positive integer n,AB^(n)=B^(n)A

Let A,B be two matrices such that they commute.Show that for any positive integer n,(AB)^(n)=A^(n)B^(n)

Let A,B be two matrices such that they commute.Show that for any positive integer n,AB^(n)=B^(n)A( ii) (AB)^(n)=A^(n)B^(n)

Let A and B are two matrices such that AB = BA, then for every n in N

If A is a nilpotent matrix of index 2, then for any positive integer n,A(I+A)^(n) is equal to A^(-1) b.A c.A^(n) d.I_(n)

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

Let Aa n dB be two 2xx2 matrices. Consider the statements (i) A B=O => A=O or B=O (ii)A B=I_2 => A=B^(-1) (iii) (A+B)^2=A^2+2A B+B^2 (i) and (ii) are false, (iii) is true (ii) and (iii) are false, (i) is true (i) is false (ii) and, (iii) are true (i) and (iii) are false, (ii) is true

If A and B are two matrices such that AB if of order n xx n, then which one of the following is correct?

Let A and B any two n xx n matrices such that the following conditions hold : AB= BA and there exist positive integers k and l such that A^(k)=I (the identity matrix) and B^(l)=0 (the zero matrix). Then-

Let A, B be two matrices different from identify matrix such that AB=BA and A^(n)-B^(n) is invertible for some positive integer n. If A^(n)-B^(n)=A^(n+1)-B^(n+1)=A^(n+1)-B^(n+2) , then