Matrix Inverse Calculator
What is Matrix Inverse
A matrix inverse is a fundamental concept in linear algebra. For a square matrix A, its inverse (denoted as A⁻¹) is another matrix that, when multiplied with A, yields the identity matrix. In mathematical notation, if A is a square matrix, then AA⁻¹ = A⁻¹A = I, where I is the identity matrix.
The inverse of a matrix exists only if the matrix is non-singular, meaning its determinant is not zero. When it exists, the inverse matrix has numerous applications in solving systems of linear equations, transforming coordinates, and various other mathematical and real-world applications.
How to Use Matrix Inverse Calculator
Step 1: Select Matrix Size
Choose the desired matrix size from the dropdown menu (2×2, 3×3, or 4×4).
Step 2: Enter Matrix Values
Fill in the matrix elements in the input fields. Each cell represents an element in your matrix. Use decimal numbers if needed.
Step 3: Verify Input
Ensure all matrix cells are filled with valid numerical values. Empty cells or invalid inputs will affect the calculation accuracy.
Step 4: Calculate
Click the calculate button to find the inverse matrix. The calculator will process your input and display the results.
Step 5: Interpret Results
Review the displayed results, which include:
- The original matrix you entered
- The calculated determinant
- The inverse matrix (if it exists)
- A step-by-step explanation of the calculation process
Step 6: Check Solution
Verify the result by multiplying your original matrix with the inverse matrix – the product should be very close to the identity matrix.
Step G: Additional Calculations
For different matrices, simply input new values or change the matrix size and repeat the process.