Let $$A$$ be a $$\,2 \times 2$$ matrix with non-zero entries and let $${A^2} = I,$$
where $$I$$ is $$2 \times 2$$ identity matrix. Define
$$Tr$$$$(A)=$$ sum of diagonal elements of $$A$$ and $$\left| A \right| = $$ determinant of matrix $$A$$.
Statement- 1: $$Tr$$$$(A)=0$$.
Statement- 2: $$\left| A \right| = 1$$ .
A
statement - 1 is true, statement - 2 is true; statement - 2 is not a correct explanation for statement - 1.
B
statement - 1 is true, statement - 2 is false.
C
statement - 1 is false, statement -2 is true
D
statement -1 is true, statement - 2 is true; statement - 2 is a correct explanation for statement - 1.
Explanation
Let $$A = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$ where $$a,b,c,d$$ $$ \ne 0$$
$${A^2} = \left( {\matrix{
a & b \cr
c & d \cr
} } \right)\left( {\matrix{
a & b \cr
c & d \cr
} } \right)$$