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=` a. `I` b. `2I` c. `O` d. -I

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)=

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 A then (A+B)^r can be expanded as binomial expansion.

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

If B and C are non-singular matrices and O is null matrix, then show that [[A, B],[ C ,O]]^(-1)=[[O, C^(-1)],[B^(-1),-B^-1A C^(-1)]]dot

If A and B are two non-singular matrices such that A B=C ,t h e n,|B| is equal to a. (|C|)/(|A|) b. (|A|)/(|C|) c. |C| d. none of these

Let A and B be two non-singular square matrices such that B ne I and AB^(2)=BA . If A^(3)-B^(-1)A^(3)B^(n) , then value of n is

Let A and B be two non-singular skew symmetric matrices such that AB = BA, then A^(2)B^(2)(A^(T)B)^(-1)(AB^(-1))^(T) is equal to

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

If the matrices, A ,B ,(A+B) are non-singular, then prove that [A(A+B)^(-1)B]^(-1)=B^(-1)+A^(-1) .