Let A be a 2 2 matrix with non-zero entries and let A^2=1 , where 1 is 2 2 identity matrix. Define Tr ( A )= sum of diagonal elements of A and |A|= determinant of matrix A . Statement-1: Tr ( A )=0 Statement-2: | A |=1

Step-by-step solution

Let A= ( array ll a & b c & d array ), a b c d 0 aligned & A^2= ( array ll a & b c & d array ) ( array ll a & b c & d array ) & A^2= ( array ll a^2+b c & a b+b d a c+c d & b c+d^2 array ) & a^2+b c=1, b c+d^2=1 & a b+b d=a c+c d=0 & c 0 and b 0 & Trace A=a+d=0 & |A|=a d-b c=-a^2-b c=-1 . aligned