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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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