By giving an example, show that `(A+B)'=A'+B'` where `A` and `B` are of same order

If AB = A and BA = B, where A and B are square matrices of same order, then

A ,\ B are two matrices such that A B and A+B are both defined; show that A ,\ B are square matrices of the same order.

Construct an example to show that f(A nn B )!= f(A) nn f(B) where A nn B != theta.

By giving a conter example , show that the statement " For any real number a and b a^(2) =b^(2) rArr a= b" is false

If A and B be two matrices such that A + B and AB are both defined, show that A and B are both square matrices of the same order.

Give an example to show that if AuuBandAcapB are given , then A and B may not be uniquely Determinable.

A,B are two matrices such that AB and A+B are both defined; show that A,B are square matrices of the same order.

If the two matrices A,B,(A+B) are non-singular (where A and B are of the same order),then (A(A+B)^(-1)B)^(-1) is equal to (A)A+B(B)A^(-1)+B^(-1)(C)(A+B)^(-1)(D)AB