If B is an idempotent matrix, and `A=I-B`, then

If A is an idempotent matrix satisfying, (I-0. 4 A)^(-1)=I-alphaA ,w h e r eI is the unit matrix of the name order as that of A , then th value of |9alpha| is equal to ________.

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 ______.

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

If A is an idempotent matrix satisfying (I-0.4A)^(-1)=I-alphaA where I is the unit matrix of the same order as that of A then the value of alpha is

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 A is a nilpotent matrix of index 2, then for any positive integer n ,A(I+A)^n is equal to A^(-1) b. A c. A^n d. I_n

If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to

If A=[[2,-2,-4],[-1,3,4],[1,-2,-3]] then A is 1) an idempotent matrix 2) nilpotent matrix 3) involutary 4) orthogonal matrix

Let B is an invertible square matrix and B is the adjoint of matrix A such that AB=B^(T) . Then

The matrix A=[-5-8 0 3 5 0 1 2-] is a. idempotent matrix b. involutory matrix c. nilpotent matrix d. none of these