Math Problem Statement

If a square matrix A satisfies A3 − 3A + 6I = 0, which of the following is equal to A−1 

Solution

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Math Problem Analysis

Mathematical Concepts

Matrix Algebra
Inverse of a Matrix
Linear Algebra

Formulas

A^3 - 3A + 6I = 0
A^{-1} = -1/6(A^2 - 3I)

Theorems

Matrix Inversion
Properties of Matrices
Cayley-Hamilton Theorem

Suitable Grade Level

Undergraduate level or advanced high school (Grades 11-12)