If `Ba n dC` 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 mxxn matrices and O is the null matrix of the type mxxn , then show that A+B=OrArr A=-B and B=-A .

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

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)

If B is a non-singular matrix and A is a square matrix,then det (B^(-1)AB) is equal to (A)det(A^(-1))(B)det(B^(-1))(C)det(A)(D)det(B)

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 B,C are n rowed square matrices and if A=B+C,BC=CB,C^(2)=O, then show that for every n in N,A^(n+1)=B^(n)(B+(n+1)C)

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