If `A^2-A+I=0,` then the invers of `A` is `A^(-2)` b. `A+I` c. `I-A` d. `A-I`

If A^2-A +I = 0 , then the inverse of A is: (A) A+I (B) A (C) A-I (D) I-A

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^3=O ,t h e nI+A+A^2 equals a. I-A b. (I+A^1)^(-1) c. (I-A)^(-1) d. none of these

If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies in the interval (a in R) a. (-2,1) b. (-1,0) c. (0,1) d. (-2,3)

If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equal to O I b. 2I c. 6I d. I

If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equal to O I b. 2I c. 6I d. I

Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=O ,t h e nf(A) is (a) I+A+A^2 (b) I+2A+2A^2 (c) I-A-A^2 (d) none of these

If A=[i-i-i i]a n dB=[1-1-1 1],t h e nA^8 equals 4B b. 128 B c. -128 B d. -64 B

If f(x) =(e^x)/(1+e^x), I_1=int(f(-a))^(f(a)) xg(x(1-x)dx, and I_2=int_(f(-a))^(f(a)) g(x(1-x))dx, then the value of (I_2)/(I_1) is (a) -1 (b) -2 (c) 2 (d) 1

A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If one vertex of the rectangle is 4+4i , then another adjacent vertex of this rectangle can be a . 2+4i b. 3+5i c. 3+3i d. 3-3i