Algebra2D

Matrices and Determinants - Theory & Concepts - Matrix Inverse

Comprehensive guide to matrix operations, calculating determinants, finding inverses, and using Cramer's Rule.

Matrix A

A = \begin{bmatrix} 2.0 & 1.0 \\ 1.0 & 2.0 \end{bmatrix}

Element a (row 1, col 1)2.0

Element b (row 1, col 2)1.0

Element c (row 2, col 1)1.0

Element d (row 2, col 2)2.0

Inverse Matrix A^-1

A^{-1} = \begin{bmatrix} 0.67 & -0.33 \\ -0.33 & 0.67 \end{bmatrix}

A^{-1} = \frac{1}{\det(A)}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}

Determinant3.00

Area Scale Factor3.00x

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