Matrix Determinant & Inverse

Input Matrix A

Calculation Results & Process

💡 Quick Guide to Determinants & Inverses

• Determinant ($\det(A)$): A scalar value defined for square matrices, corresponding to the scaling factor of area or volume under the linear transformation represented by the matrix.
• Inverse Matrix ($A^{-1}$): A matrix that, when multiplied by the original matrix $A$, results in the identity matrix $I$ ($A \cdot A^{-1} = A^{-1} \cdot A = I$). A matrix with a determinant of $\det(A) = 0$ is called "singular" and does not have an inverse.
• Gauss-Jordan Elimination: By setting up the augmented matrix $[A | I]$ and performing elementary row operations to transform the left side into the identity matrix $I$, the resulting right side will be the inverse matrix $A^{-1}$.