## Math Problem Statement

P = [[1, 2, 2], [- 3, - 1, 1], [13, - 4, - 2]] Inverse

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Linear Algebra

Matrix Inversion

### Formulas

Inverse of a matrix: P^{-1} = adj(P) / det(P)

Determinant formula for a 3x3 matrix

Adjugate matrix for finding the inverse

### Theorems

A matrix has an inverse if and only if its determinant is non-zero

Cramer's rule (used in solving systems of equations via matrix inversion)

### Suitable Grade Level

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

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