If A and B are two nonsingular matrices of the same order such that `B^(r)=I`, for some positive integer `r gt 1`, then `A^(-1) B^(r-1) A-A^(-1) B^(-1) A=`

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

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 , B are two square matrices of same order such that A+B=AB and I is identity matrix of order same as that of A , B , then

If A and B are two non-singular matrices which commute, then (A(A+B)^(-1)B)^(-1)(AB)=

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 square matrices such that B=-A^(-1)BA , then (A+B)^(2) is equal to

If A and B are two non-singular matrices of order 3 such that A A^(T)=2I and A^(-1)=A^(T)-A . Adj. (2B^(-1)) , then det. (B) is equal to

Let A and B are two square matrices of order 3 such that det. (A)=3 and det. (B)=2 , then the value of det. (("adj. "(B^(-1) A^(-1)))^(-1)) is equal to _______ .

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

If A and B are square matrices of order 3 such that det. (A) = -2 and det.(B)= 1 , then det.(A^(-1)adjB^(-1).adj(2A^(-1)) is equal to