We know that Det(A) = product of eigen values and Tr(A) = sum of eigen values. Therefore, to have both eigen values as positive , det(A) should be >0 & Tr(A) >0.So, we can check for both the conditions on the given matrix:
Det(A) > 0 => 2k-1>0 => k>1/2
and Tr(A) > 0 => k+2 > 0 => k>-2
Hence, the first solution satisfies both the condition. So, the answer is A) .. I think this is a better approach than the Best Answer here @Joshi_nitish