1. **State the problem:** We want to simplify a large determinant into the product of two factors. 2. **Formula and rules:** The determinant of a matrix can sometimes be factored if the matrix has a block structure or special properties. Key rules include: - If a matrix is block diagonal, its determinant is the product of the determinants of the blocks. - Row and column operations can simplify the determinant without changing its value (except for sign changes). 3. **Step-by-step approach:** - Identify if the matrix can be partitioned into smaller blocks. - Use row and column operations to create zeros in strategic places to isolate blocks. - Calculate the determinant of each block separately. - Multiply these determinants to get the determinant of the original matrix. 4. **Example:** Suppose the matrix is block diagonal: $$\begin{pmatrix} A & 0 \\ 0 & B \end{pmatrix}$$ Then: $$\det\begin{pmatrix} A & 0 \\ 0 & B \end{pmatrix} = \det(A) \times \det(B)$$ 5. **Summary:** Simplifying a big determinant into two factors involves recognizing block structures or applying row/column operations to factor the matrix into simpler parts whose determinants multiply to the original determinant.