Matrix Calculator
Perform matrix operations with this matrix calculator. Supports addition, subtraction, multiplication, transpose, determinant, and inverse.
About Matrix Calculator
This matrix calculator handles the most common linear algebra operations in one tool. Enter values for two matrices and choose from addition, subtraction, multiplication, transpose, determinant, or inverse.
Supported Operations
For two-matrix operations, choose A + B, A - B, or A * B. For single-matrix operations, pick transpose, determinant, or inverse for either matrix. The tool checks dimension compatibility and handles edge cases like singular matrices gracefully.
Step-by-Step Determinants
When computing a determinant for 2x2 or 3x3 matrices, the calculator shows each step of the cofactor expansion. This makes it useful for checking homework or understanding how determinant computation works.
Quick Fill and Flexibility
Use the Identity, Zero, or Random buttons to quickly populate a matrix. Adjust dimensions from 1x1 up to 5x5 at any time. If you need to solve equations, the Equation Solver handles systems of linear equations. For statistical work, try the Standard Deviation Calculator. All calculations run entirely in your browser.
Frequently Asked Questions
What matrix sizes are supported?
You can work with matrices from 1x1 up to 5x5. Adjust the row and column count using the dropdown selectors next to each matrix label.
What operations are available?
You can add, subtract, or multiply two matrices. Single-matrix operations include transpose, determinant (for square matrices), and inverse (for non-singular square matrices). Each operation checks dimensions automatically.
What happens if my matrix has no inverse?
A matrix with a determinant of zero is called singular and has no inverse. The calculator will display a clear message explaining this. You can check the determinant first to see if an inverse exists.
Does it show step-by-step work?
Yes, the determinant operation includes a step-by-step cofactor expansion for 2x2 and 3x3 matrices. This helps you follow the calculation and verify your own work.
Why can't I multiply these two matrices?
Matrix multiplication requires the number of columns in matrix A to equal the number of rows in matrix B. For example, a 2x3 matrix can multiply a 3x2 matrix, but not a 2x2. The calculator shows a clear error when dimensions don't match.