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 + I = [(3,-2),(4,1)] , then (A+I) (A-I) is equal to

If A+2I= [(6,2),(3,-4)] ,then A(A+I)=

If a^2+b^2=1 t h e n (1+b+i a)/(1+b-i a)= 1 b. 2 c. b+i a d. a+i b

If A=[[a+i b, c+i d],[-c+i d, a-i b]]a n da^2+b^2+c^2+d^2=1,t h e nA^(-1) is equal to a. [[a+i b,-c+i d],[-c+i d, a-i b]] b. [[a-i b,-c-i d],[-c-i d, a+i b]] c. [[a+i b,-c-i d],[-c+i d, a-i b]] 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 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 Aa n dB are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e nA^(-1)B^(r-1)A=A^(-1)B^(-1)A= I b. 2I c. O d. -I

If A^(3)=O , then prove that (I-A)^(-1) =I+A+A^(2) .

If A is a 2xx2 matrix such that A^(2)-4A+3I=O , then prove that (A+3I)^(-1)=7/24 I-1/24 A .