Inverse Matrix Calculator with Steps

Free online inverse matrix calculator with step-by-step solutions. See detailed steps for calculating matrix inverse using Gauss-Jordan elimination. Perfect for learning linear algebra.

How to Use the Inverse Matrix Calculator with Steps

  1. Select the matrix size (2×2, 3×3, or 4×4)
  2. Enter the values for each element of the matrix
  3. Click "Calculate with Steps" to see the detailed solution
  4. Review each step of the calculation process
  5. The final inverse matrix will be displayed

This calculator shows the complete step-by-step process, making it perfect for learning how to calculate matrix inverses manually.

Calculation Methods

The calculator uses different methods depending on the matrix size:

  • 2×2 matrices: Direct formula method - A⁻¹ = (1/det) × [[d, -b], [-c, a]]
  • 3×3 and 4×4 matrices: Gauss-Jordan elimination method - transforms [A|I] into [I|A⁻¹]

The Gauss-Jordan elimination method involves:

  1. Creating an augmented matrix [A | I]
  2. Using row operations to transform A into the identity matrix
  3. The right side becomes the inverse matrix

Frequently Asked Questions

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