JEE Main 2008 Mathematics question

Let A be a matrix with real entries. Let I be the identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that . Statement -1: If and , then det . Statement −2 : If and , then .

• (1)Statement −1 is false, Statement −2 is true
• (2)Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
• (3)Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1
• (4)Statement −1 is true, Statement −2 is false.Correct