Lang
Interactive mathematics
Matrix Calculator
Build matrices cell by cell, calculate with clear steps, and see how a two-dimensional matrix transforms a grid.
Thirteen operations · worked steps · visual transformationBuild your matrices
Choose the rows and columns. Type into the cells or paste rows copied from a spreadsheet.
Matrix A
Paste rows
Use new lines for rows and tabs, spaces or semicolons between numbers.
Matrix B
Paste rows
Use new lines for rows and tabs, spaces or semicolons between numbers.
All results
Results are rounded for display; calculations keep full numerical precision.
Add A + B
How it was calculated
Subtract A − B
How it was calculated
Multiply A × B
How it was calculated
Inverse of A
How it was calculated
Inverse of B
How it was calculated
Transpose A
How it was calculated
Transpose B
How it was calculated
Determinant of A
How it was calculated
Determinant of B
How it was calculated
Rank of A
How it was calculated
Rank of B
How it was calculated
Reduced row echelon form of A
How it was calculated
Reduced row echelon form of B
How it was calculated
2D matrix transformation
Move the slider to see how the selected matrix transforms the unit square and coordinate grid.
Original unit squareTransformed square
This picture represents the linear transformation of the selected 2×2 matrix; it does not display addition or multiplication of matrices.
Understand matrix operations
Addition and subtraction
Only matrices of the same size can be added or subtracted. Each answer cell combines the cells in the same position.
Matrix multiplication
The inner dimensions must match. An answer cell is a row–column dot product, so changing the order can change the result.
Inverse and determinant
An inverse exists only for a square matrix with a nonzero determinant. A one-by-one matrix can also have an inverse.
Rank and row reduction
Rank counts independent rows or columns. Reduced row echelon form exposes pivots and helps reveal dependencies.
Related mathematics tools
Explore equations, vectors and other numerical tools.
Frequently asked questions
Can I paste a matrix from a spreadsheet?
Yes. Copy a rectangular range and paste it into the box for A or B. Tabs and line breaks are recognized.
Why does multiplication reject my matrices?
The number of columns in A must match the number of rows in B. The answer then has A’s row count and B’s column count.
When does an inverse exist?
A square matrix is invertible when its determinant is not zero. A one-by-one matrix has inverse 1/a when its entry a is not zero.
Why does the transformation picture disappear?
The visual guide is only for two-by-two matrices with values that fit a readable coordinate view.
What does rank mean?
Rank is the number of independent rows or columns, found from the pivot positions of a row-reduced matrix.