If `B` is an idempotent matrix, and `A=I-B ,` then a. `A^2=A` b. `A^2=I` c. `A B=O` d. `B A=O`

If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to a. B A b. -B A c. I d. O

If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to B A b. -B A c. I d. O

If Z is an idempotent matrix, then (I+Z)^n I+2^n Z b. I+(2^n-1)Z c. I-(2^n-1)Z d. none of these

If for the matrix A ,\ A^3=I , then A^(-1)= (a) A^2 (b) A^3 (c) A (d) none of these

If [a b c1-a] is an idempotent matrix and f(x)=x-^2=b c=1//4 , then the value of 1//f(a) is ______.

A square matix A is called idempotent if (A) A^2=0 (B) A^2=I (C) A^2=A (D) 2A=I

If A is non-diagonal involuntary matrix, then A-I=O b. A+I=O c. A-I is nonzero singular d. none of these

If A is a square matrix such that A^2=I , then (A-I)^3+(A+I)^3-7A is equal to: (A) A (B) I-A (C) I+A (d) 3A

In a triangle A B C ,\ A C > A B , D is the mid-point of B C and A E_|_B C . Prove that: (i) A B^2=A D^2-B C* D E+1/4B C^2

If the matrix A B is zero, then It is not necessary that either A=O or, B=O (b) A=O or B=O (c) A=O and B=0 (d) all the above statements are wrong