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

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,B,C are non - singular matrices of same order then (AB^(-1)C)^(-1)=

Prove that: (a^(-1)+b^(-1))^(-1)=(a b)/(a+b)

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

If A, B are two n xx n non-singular matrices, then (1) AB is non-singular (2) AB is singular (3) (AB)^(-1)=A^(-1) B^(-1) (4) (AB)^(-1) does not exist

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

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

For non-singular square matrix A ,\ B\ a n d\ C of the same order then, (A B^(-1)C)^(-1)= (a) A^(-1)B C^(-1) (b) C^(-1)B^(-1)A^(-1) (c) C B A^(-1) (d) C^(-1)\ B\ A^(-1)

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; B are invertible matrices of the same order; then show that (AB)^-1 = B^-1 A^-1