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
- Select the matrix size (2×2, 3×3, or 4×4)
- Enter the values for each element of the matrix
- Click "Calculate with Steps" to see the detailed solution
- Review each step of the calculation process
- 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:
- Creating an augmented matrix [A | I]
- Using row operations to transform A into the identity matrix
- The right side becomes the inverse matrix
Frequently Asked Questions
Cite This Calculator
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