Let `A ,B` be two matrices such that they commute, then for any positive integer `n ,`
(i) `A B^n=B^n A`
(ii)`(A B)^n =A^n B^n`

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

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

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

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

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

If Aa n dB are square matrices of the same order and A is non-singular, then for a positive integer n ,(A^(-1)B A)^n is equal to A^(-n)B^n A^n b. A^n B^n A^(-n) c. A^(-1)B^n A^ d. n(A^(-1)B^A)^

If A and B are two matrices such that rank of A = m and rank of B = n, then

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

Statement 1: Let A ,B be two square matrices of the same order such that A B=B A ,A^m=O ,n dB^n=O for some positive integers m ,n , then there exists a positive integer r such that (A+B)^r=Odot Statement 2: If A B=B At h e n(A+B)^r can be expanded as binomial expansion.

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