{
  "problem": "If $\\det \\mathbf{A} = 4$ and $\\det \\mathbf{B} = -5,$ then find $\\det (\\mathbf{A}\\mathbf{B}).$",
  "prefixes": [
    "Recall that the determinant of a product satisfies $\\det(AB)=\\det(A)\\det(B)$. Substituting the values gives $4\\cdot(-5)$.",
    "Recall that the determinant of a product satisfies $\\det(AB)=\\det(A)+\\det(B)$. Substituting the values gives $4+(-5)$."
  ]
}