If A = [[sin2θ, 2sin²θ – 1, 0],[cos2θ, 2sinθ cosθ, 0],[0, 0, 1]], then which of the following statements is/are correct? 1. A⁻¹ = adj A 2. A is skew-symmetric matrix 3. A⁻¹ = Aᵀ. Select the correct answer using the code given below:

Note 2sin²θ – 1 = –cos2θ and 2sinθcosθ = sin2θ. So A = [[sin2θ, –cos2θ, 0],[cos2θ, sin2θ, 0],[0,0,1]]. This is an orthogonal matrix (rotation matrix in 2D extended). det(A) = sin²2θ + cos²2θ = 1. For orthogonal matrices with det = 1, A⁻¹ = Aᵀ. Also adj A = det(A)·A⁻¹ = A⁻¹. A is not skew-symmetric since diagonal entries are non-zero. So statements 1 and 3 are correct.