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How to solve this problem- - Matrices and Determinants - JEE Main-2

Directions : Question is Assertion - ­Reason type. This question contains two statements : Statement - 1 (Assertion) and Statement­-2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Question: Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr(A) , the sum of diagonal entries of A . Assume that A^{2}=I.

Statement - 1 :  If  A\neq I\; and\; A\neq -I,then\; det\; A=-1.

Statement - 2 : If A\neq I\; and\; A\neq -I,then\; tr(A)\neq 0

 

  • Option 1)

    Statement -1 is true, Statement­-2 is false

  • Option 2)

    Statement-­1 is false, Statement­-2 is true ;

  • Option 3)

    Statement­-1 is true, Statement­-2 is true Statement­-2 is a correct explanation for Statement­-1

  • Option 4)

    Statement­-1 is true, Statement­-2 is true Statement-­2 is not a correct explanation for Statement­-1

 
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