How to use the matrix calculator
Set dimensions and choose an operation
- Choose Add / Subtract, Multiply, Transpose, Determinant, Inverse, Rank, or Solve Ax = b.
- Set Rows and Cols for Matrix A. When the operation uses Matrix B, set its Rows and Cols as well.
- Fill each generated cell with a signed number, decimal, or simple fraction. For Solve Ax = b, enter one value per row in the Ax = b inputs.
- For Add / Subtract, choose A + B or A − B, then click Calculate to show the result and Steps.
- Click Reset to rebuild the current grids. Use Copy result or Download result (.txt) to save the result summary.
How addition, multiplication, and transpose differ
Add / Subtract requires Matrix A and Matrix B to have matching dimensions. Multiply sets Matrix B's Rows to Matrix A's Cols, while you choose Matrix B's Cols. Transpose takes Matrix A and turns its rows into columns.
[1 2; 3 4] + [5 6; 7 8]
[6 8; 10 12]The first line shows the input matrices and operation. The second line shows the result. Each result entry stays a reduced fraction, so 3/4 remains exact instead of becoming a rounded decimal.
What Determinant, Inverse, Rank, and Solve Ax = b show
Determinant and Inverse require square Matrix A, so the tool keeps Cols equal to Rows in those modes. Determinant uses forward row elimination. Inverse uses Gauss-Jordan reduction on [A | I]. Rank reduces Matrix A to row-reduced form and counts its pivot columns.
A singular matrix has determinant 0 and has no inverse. Solve Ax = b also requires square Matrix A. The result can be a unique solution, infinitely many solutions with free variables, or no solution when a row becomes a contradiction. The Steps list shows the row operations.
What entries the matrix calculator accepts
Each cell accepts a signed integer, decimal, or simple fraction such as -3, 2.5, or 3/4. Empty cells, zero denominators, variables, expressions such as 2+3, and other symbols trigger a validation error. The dimension controls limit each matrix to 6 × 6.
Changing the operation or dimensions rebuilds the grids and hides the previous result. Reset clears the result and error while keeping the selected operation. The calculation runs in the browser, and the script makes no request containing the matrix entries.
Tasks the matrix calculator can check
- Check a matrix addition by entering two same-size matrices and reading the exact result and Steps list.
- Test a transformation matrix with Multiply or Transpose, then save the result as
matrix-result.txt. - Work through a linear system by entering its coefficient matrix in Matrix A and its constants in the Ax = b inputs, then following the row reductions under Steps.
When to choose a different calculator
Choose this Matrix Calculator when you need several matrix operations in one place or want to solve Ax = b from Matrix A and the Ax = b inputs. For a determinant-only task on a square matrix up to 8x8, use the Matrix Determinant Calculator; for an inverse-only task, use the Matrix Inverse Calculator. If your problem is written as equations such as 2x + y = 5, the Algebra Calculator is the better match. Other Math Calculators cover jobs outside matrix operations.
Frequently asked questions
How do I add two matrices in the Matrix Calculator?
Select Add / Subtract, make Matrix A and Matrix B the same size, choose A + B, fill every cell, and click Calculate. The result and Steps appear below the input.
Can the Matrix Calculator find an inverse and determinant?
The Matrix Calculator finds both from square Matrix A. A singular matrix returns determinant 0 and a no-inverse status. An invertible matrix returns the inverse matrix.
How do I solve Ax = b with the Matrix Calculator?
Select Solve Ax = b, enter the square coefficient matrix in Matrix A, and enter one constant per row in the Ax = b inputs. The result identifies a unique solution, infinitely many solutions, or no solution.
What does the Matrix Calculator reject?
It rejects empty cells, zero denominators, variables, expressions, and unsupported symbols. Use signed numbers, decimals, or simple fractions such as 3/4 in matrices up to 6 × 6.