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Let A be a 2 xx 2 matrix with non-zero e...

Let A be a `2 xx 2` matrix with non-zero entries and let A^2=I, where i is a `2 xx 2` identity matrix, Tr(A) i= sum of diagonal elements of A and `|A|` = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2:`|A|`=1

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Let `A = [[a,b],[c,d]]`
It is given that,
`A^2 = I`
`:. [[a,b],[c,d]][[a,b],[c,d]] = [[1,0],[0,1]]`
`=>[[a^2+bc,ab+bd],[ac+cd,bc+d^2]]= [[1,0],[0,1]]`
`=>a^2+bc = 1->(1)`
`=>ab+bd = 0 =>b(a+d) = 0 => a = -d->(2) ...[As b!=0]`
So, we can write,
...
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