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Inverse Matrix

High School

Definition

Matrix B such that AB = BA = I, where I is the identity matrix.

Formulas

AA⁻¹ = A⁻¹A = I

Definition of inverse

A⁻¹ = (1)/(det(A)) \beginpmatrix d & -b \\ -c & a \endpmatrix

Inverse of 2×2 matrix (det(A) ≠ 0)

Examples

Example 1

Find the inverse of A = [[2, 1], [5, 3]].

Applications

Systems of equations

Ax = b → x = A⁻¹b

Cryptography

Matrix encryption

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