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