Let `A` and `B` be two `2xx2` matrices. Consider the statements (i) `A B=0 => A=0 or B=0` (ii)`AB=I_2 => A=B^(-1)` (a) only (i) (b) only (ii) (c) both are correct (d) none of these.

Let Aa n dB be two 2xx2 matrices. Consider the statements (i) A B=O => A=OorB=O (ii) A B=I_2 =>A=B^(-1) (iii) (A+B)^2=A^2+2A B+B^2 (a)(i) and (ii) are false, (iii) is true (b)(ii) and (iii) are false, (i) is true (c)(i) is false (ii) and, (iii) are true (d)(i) and (iii) are false, (ii) is true

A and B be 3xx3 matrices such that AB+A+B=0 , then

In frog, teeth occur on (a) lower jaw only (b) upper jaw only (c) both a and b (d) none of the above

If A and B are two matrices such that AB=B and BA=A , then A^2+B^2=

Let A ,B be two matrices such that they commute, then for any positive integer n , (i) A B^n=B^n A (ii) (A B)^n =A^n B^n

If A ne 0 and B ne 0 are two 2xx2 matrices such that AB = 0, then which of the following is correct ?

If A and B are two matrices of order 3 such that AB=O and A^(2)+B=I , then tr. (A^(2)+B^(2)) is equal to ________.

Let a and b be two real numbers such that a > 1, b >1. If A=((a,0),(0,b)), then (lim)_(n->oo) A^-n is (a) unit matrix (b) null matrix (c) 2I (d) non of these

The number of 2xx2 matrices A , that are there with the elements as real numbers satisfying A+A^(T)=I and A A^(T)=I is (a) zero (b) one (c) two (d) infinite

Let A and B be two non-singular square matrices such that B ne I and AB^(2)=BA . If A^(3)-B^(-1)A^(3)B^(n) , then value of n is