Under which of the following conditions does the determinant of the matrix given below vanish (equal zero)? |a b c| |b c a| |c a b| 1. a + b + c = 02. a3 + b3 + c3 = 3abc3. a2 + b2 + c2 - ab - bc - ca = 0 Select the correct answer using the code given below:

If A is a square matrix of order n, then the determinant of its adjoint matrix, |adj(A)|, is equal to:

If A is a non-singular 3 × 3 matrix and det(ATA) = 16, then det(A) is equal to:

If the minimum and the maximum values of the function f: [π/4, π/2] → R, defined by the determinant of the matrix given below are m and M respectively, then the ordered pair (m, M) is equal to: f(θ) = det -sin2θ-1-sin2θ1-cos2θ-1-cos2θ11210-2