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

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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

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Let A = ( a c ​ b d ​ ) , ab c d  = 0 ​ A 2 = ( a c ​ b d ​ ) ⋅ ( a c ​ b d ​ ) ⇒ A 2 = ( a 2 + b c a c + c d ​ ab + b d b c + d 2 ​ ) ⇒ a 2 + b c = 1 , b c + d 2 = 1 ab + 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. ​

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