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

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

If a and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

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 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 square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

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

If A is a 3xx3 non -singular matrix such that "AA"^(T)=A^(T)A "and" B=A^(-1)A^(T), "then" BB^(T) =

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 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