Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Matrix Factorization
Modular Arithmetic
Determinants
Matrix Product

Formulas

det(A) = det(B) * det(C)
det(C) ≡ 1 (mod 3)
det(B) ≡ det(A) (mod 3)

Theorems

The determinant of a product of matrices
Modular determinant properties

Suitable Grade Level

University Level (Linear Algebra)