Let AAA be a 2×22 \times 22×2 matrix with det(A)=6\det(A) = 6det(A)=6. Consider the matrix B=2A2−3AB = 2A^2 - 3AB=2A2−3A. Which statement is correct?
det(B)=2(det(A))2−3det(A)=2(36)−18=54\det(B) = 2(\det(A))^2 - 3\det(A) = 2(36) - 18 = 54det(B)=2(det(A))2−3det(A)=2(36)−18=54
det(B)=2⋅6−3⋅6=−18\det(B) = 2 \cdot 6 - 3 \cdot 6 = -18det(B)=2⋅6−3⋅6=−18
Cannot be determined; the determinant of a matrix polynomial depends on the specific entries of AAA, not just det(A)\det(A)det(A)
det(B)=0\det(B) = 0det(B)=0 because BBB is singular