Inverse Matrix Calculator
Free online inverse matrix calculator to find the inverse of any square matrix. Calculate matrix inverse instantly for 2x2, 3x3, and 4x4 matrices. Perfect for linear algebra and engineering.
How to Use the Inverse Matrix Calculator
- Select the matrix size (2×2, 3×3, or 4×4)
- Enter the values for each element of the matrix
- Click "Calculate Inverse" to compute the inverse matrix
- The inverse matrix will be displayed if it exists
Note: Only square matrices with a non-zero determinant have an inverse. If the determinant is zero, the matrix is singular and has no inverse.
What is an Inverse Matrix?
The inverse of a matrix A (denoted as A⁻¹) is a matrix such that when multiplied by A, it produces the identity matrix I:
A × A⁻¹ = I
Not all matrices have an inverse. A matrix must be:
- Square: The number of rows must equal the number of columns
- Non-singular: The determinant must not be zero
Inverse matrices are essential in solving systems of linear equations, finding transformations, and many other applications in mathematics, engineering, and computer science.
Common Uses
- Solving systems of linear equations
- Finding matrix transformations
- Computer graphics and 3D transformations
- Cryptography and encoding
- Engineering calculations and simulations
Frequently Asked Questions
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