Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Determinants
Matrix Transposition
Matrix Inversion

Formulas

det(A^2) = det(A)^2
det(B^T) = det(B)
det(A^{-1}) = 1/det(A)

Theorems

Determinant of the product of matrices: det(AB) = det(A) * det(B)
Determinant of a transpose: det(B^T) = det(B)
Determinant of an inverse matrix: det(A^{-1}) = 1/det(A)

Suitable Grade Level

University-level Linear Algebra