Matrix Inverse Calculator | Fast & Free

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.

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