Let A and B be two `2 xx 2` matrix with real entries, If AB=0 and such that tr(A)=tr(B)=0then

Let A = (a_(ij)_(3xx2) be a 3xx2 matrix with real entries and B = AA. Then

Let A be a 2xx2 matrix with real entries. Let I be the 2xx2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2=""I . Statement 1: If A!=I and A!=""-I , then det A""=-1 . Statement 2: If A!=I and A!=""-I , then t r(A)!=0 .

9, Let A be a 2 x 2 matrix with real entries. Let I be the 2 × 2 2identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 -1 nvo bud o malai Statement 1: If A 1 and A?-1, then det A =-1. Statement 2: If A 1 and A?-I, then tr (A)?0 A. Statement 1 is false, statement 2 is true. B. Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 . C. Statement 1 is true, statement 2 is true; statement 2 is nota correct explanation for statement 1. D. Statement 1 is true, statement 2 is false.

Let A be a 2 xx 2 real matrix with entries from { 0,1} and |A| ne 0 . Consider the following two statements : (P ) If A ne I_2 then |A| =-1 (Q ) if |A| =1 , then Tr (A)=2 Where I_2 denotes 2xx 2 identity matrix and tr (A) denotes the sum of the diagonal entries of A then :

Suppose A and B are two 3xx3 non singular matrices such that tr (AB) = 7.57 then tr (BA+I_(3)) = ______