If A, B are two square matrices such that AB = A and BA = B, then prove that `B^(2) = B`

If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

If A and B are two matrices such that AB = A and BA = B then B is equal to__

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)) .

If A and B are square matrices of same order such that AB=O and B ne O , then prove that |A|=0 .

If A and B are square matrices of same order such that AB+BA=O , then prove that A^(3)-B^(3)=(A+B) (A^(2)-AB-B^(2)) .

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 square matrices of the same order such that AB = A and BA = B, then……

If A and B are two matrices such that A + B and AB are both defined, then:

If A and B are square matrices of order 3 such that |A| = 3 and |B| = 2 , then find the value of |A^(-1) adj(B^(-1)) adj (2A^(-1))|

If A and B are two square matrices of the same order such that AB = A, BA = B and if a matrix A is called idempotent if A^(2)=A , then