Choose the correct statement(s) for same order square matrices A & B, `(I+A^-1)^-1=A(A+I)^-1;|I+A^-1| != ,|A+I| !=0`

Choose the correct statement related to the matrices A=[[1,0],[0,1]] , B=[[0,1],[1,0]]

If A and B are square matrices of the same order and AB=3I , then A^(-1)=

A and B are two square matrices of same order. If AB =B^(-1), " then " A^(-1) =____.

If A^3 =O, then I+ A + A^2 = (where I is the unit matrix of order same as that of square matrix A) is equals (A) I -A (B) (I-A)^-1 (C) (I+A) (D) none of these

If A=[(a,b),(0,a)] is nth root of I_(2) , then choose the correct statements : (i) if n is odd, a=1, b=0 (ii) if n is odd, a=-1, b=0 (iii) if n is even, a=1, b=0 (iv) if n is even, a=-1, b=0

If A a n d B are two non-singular matrices of the same order such that B^r=I , for some positive integer r >1,t h e n (A^(-1)B^(r-1)A)-(A^(-1)B^(-1)A)= a. I b. 2I c. O d. -I

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 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 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 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= a. I b. 2I c. O d. -I