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

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

If A and B are square matrices of the same order and AB=3I , then A^(-1)=

If A and B are symmetric non-singular matrices of same order,AB = BA and A^(-1)B^(-1) exist, prove that A^(-1)B^(-1) is symmetric.

If A and B be two non singular matrices and A^(-1) and B^(-1) are their respective inverse, then prove that (AB)^(-1)=B^(-1)A^(-1)

Suppose A and B are two non-singular matrices of order n such that AB=BA^(2) and B^(5)=I ,then which of the following is correct

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 and B are square matrices of the same order and A is non-singular,then for a positive integer n,(A^(-1)BA)^(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)BA)