Find the Matrix Inverse

Enter square matrix dimensions, generate input matrix $A$, fill values, and calculate inverse using augmented matrix $[A | I]$.
Matrix entries can be real or complex, e.g. 3+2i, -1/2-i, 0.2i, etc.
(Matrix must be square)

For a square matrix $A$, the inverse $A^{-1}$ satisfies:

$ A \cdot A^{-1} = A^{-1} \cdot A = I $

Existence:

$A^{-1}$ exists if and only if $\det(A) \neq 0$ (matrix is invertible or non-singular)
If $\det(A) = 0$, the matrix is singular and has no inverse

Computing via Gauss-Jordan:

Form the augmented matrix $[A | I]$ and row-reduce to $[I | A^{-1}]$

Properties:

$(A^{-1})^{-1} = A$
$(AB)^{-1} = B^{-1}A^{-1}$
$(A^T)^{-1} = (A^{-1})^T$

Matrix size:

Display Values as: Fraction Decimal

Find the Matrix Inverse

About Matrix Inverse