1. Let's start by stating the problem: We need to find the determinants of matrices B and C. 2. The determinant of a matrix is a scalar value that can be computed from the elements of a square matrix and encodes certain properties of the matrix. 3. For a 2x2 matrix $ \begin{bmatrix} a & b \\ c & d \end{bmatrix} $, the determinant is calculated as: $$\det = ad - bc$$ 4. For larger matrices, the determinant can be calculated using cofactor expansion or other methods. 5. Since the matrices B and C are not provided, please provide the matrices B and C so I can calculate their determinants.