MathTools

Matrix Inversion

Type in a square matrix of integers or fractions and get its exact inverse back. Every row operation of the Gauss–Jordan elimination is listed underneath.
Not invertible
Matrix is singular (determinant = 0) and cannot be inverted.
Input matrix Afractions allowed

Integers, negatives, decimals or fractions (e.g. 3, -2, 1/2). Empty cells count as 0.

Step-by-step solution

  1. 1

    Augment with the identity

    Form the block matrix [A | I]. Reducing the left half to the identity will reveal A⁻¹ on the right.

    0
    0
    0
    1
    0
    0
    0
    0
    0
    0
    1
    0
    0
    0
    0
    0
    0
    1
  2. 2

    Column 1: no non-zero pivot

    Every candidate pivot in this column is zero, so A is singular.

    0
    0
    0
    1
    0
    0
    0
    0
    0
    0
    1
    0
    0
    0
    0
    0
    0
    1