LetA be a `2xx2`matrix with real entries. Let I be the `2xx2`identity matrix. Denote by tr (A), the sumof diagonal entries of A. Assume that `A^2=""I`.Statement1: If `A!=I`and `A!=""-I`, then det `A""=-1`.Statement2: If `A!=I`and `A!=""-I`,then `t r(A)!=0`.(1)Statement 1is false, Statement `( 2) (3)-2( 4)`is true(6)Statement 1is true, Statement `( 7) (8)-2( 9)`(10)is true, Statement `( 11) (12)-2( 13)`is a correct explanation forStatement 1(15)Statement 1is true, Statement `( 16) (17)-2( 18)`(19)is true; Statement `( 20) (21)-2( 22)`is not a correct explanationfor Statement 1.(24)Statement 1is true, Statement `( 25) (26)-2( 27)`is false.A. Statement - 1 is true, statement - 2 is true and statement -2 is correct explanation for statement - 1.B. Statement - 1 is true, statement - 2 is true and statement -2 is NOT the correct explanation for statement - 1.C. Statement -1 is true, statement -2 is false.D. Statement -1 is false, statement -2 is true.

LetA be a `2xx2`matrix with real entries. Let I be the `2xx2`identity

1.	LetA be a `2xx2`matrix with real entries. Let I be the `2xx2`identity matrix. Denote by tr (A), the sumof diagonal entries of A. Assume that `A^2=""I`.Statement1: If `A!=I`and `A!=""-I`, then det `A""=-1`.Statement2: If `A!=I`and `A!=""-I`,then `t r(A)!=0`.(1)Statement 1is false, Statement `( 2) (3)-2( 4)`is true(6)Statement 1is true, Statement `( 7) (8)-2( 9)`(10)is true, Statement `( 11) (12)-2( 13)`is a correct explanation forStatement 1(15)Statement 1is true, Statement `( 16) (17)-2( 18)`(19)is true; Statement `( 20) (21)-2( 22)`is not a correct explanationfor Statement 1.(24)Statement 1is true, Statement `( 25) (26)-2( 27)`is false.A. Statement - 1 is true, statement - 2 is true and statement -2 is correct explanation for statement - 1.B. Statement - 1 is true, statement - 2 is true and statement -2 is NOT the correct explanation for statement - 1.C. Statement -1 is true, statement -2 is false.D. Statement -1 is false, statement -2 is true.
Answer» Correct Answer - C

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