Question

Let A be a 2x2 matrix with non zero entries and let A2 = I, where I is 2x2 identity matrix.

Define Tr(A) = sum of diagonal elements of A and = determinant of matrix A.

Statement 1: Tr(A) = 0

Statement 2: = -1

A) Statement 1 is false, statement 2 is true.

B) Statement 1 is true, statement 2 is true; Statement 2 is correct explanation for statement 1.

C) Statement 1 is true, statement 2 is true; Statement 2 is not correct explanation for statement1.

D) Statement 1 is true, statement 2 is false.​

Answer 1

Answer:

$Let A=( ac​ bd​ ), abcd =0A 2 =( ac​ bd​ )⋅( ac​ bd​ )A 2 =( a 2 +bcac+cd​ ab+bdbc+d 2 ​ )=a 2 + bc =1, bc +d 2 =1ab+bd=ac+cd=0c=0 and b=0=a+d=0Trace A=a+d=0⇒a=−d∣A∣=ad− bc =−a 2 − bc =−1 Hence, option 'B' is correct.$

Step-by-step explanation:

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