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 ,\ 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 , (i) A B^n=B^n A (ii) (A B)^n=A^nB^n

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

If A is a square matrix such that |A| = 2 , then for any positive integer n, |A^(n)| is equal to

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

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)^

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.

If A a n d B are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e n (A^(-1)B^(r-1)A)-(A^(-1)B^(-1)A)= a. I b. 2I c. O d. -I