Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra

Let A = M2(ℝ) be a matrix which is not a diagonal matrix. Then which of the following is/are correct 

1
If tr(A) = -1 and det(A) = 1 then A3 = I
2
If A3 = I then  tr(A) = -1 and det(A) = 1 
3
If A3 = I then A is diagonalizable over ℂ. 
4
If A3 = I then A is diagonalizable over ℝ
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