Mathematical Tools

Active tool: Matrix Calculator

Selected option: Results update automatically

What It Does

Adds, subtracts, multiplies, transposes, and inverts matrices, and computes determinants and rank — up to 8×8 — showing the row-reduction steps for determinants and inverses. Everything runs in your browser.

How to Use It

  1. Pick an operation.
  2. Set the dimensions and type the matrix entries into the grid(s).
  3. Read the result; expand Steps to see the working (determinant/inverse).
  4. Copy or export the result.

Options Explained

OptionDescription
OperationAdd, subtract, scalar-multiply, multiply, transpose, determinant, inverse, rank.
DimensionsRows/cols of each matrix (1–8); the tool keeps them compatible per operation.
ScalarThe multiplier for the k·A operation.
PrecisionHow many significant digits to show.
StepsShow the working for each operation, including row-reduction, dot-product multiplication, and the final transformed matrix.
💡 Tip: Only square matrices have a determinant or inverse, and a matrix is invertible exactly when its determinant is non-zero.
Matrices
Matrix A
Matrix B

Result

Result matrix
Row / ColumnColumn 1Column 2
Row 100
Row 200

Steps

  1. Matrix A (m×n)
    Matrix A (m×n)
    Row / ColumnColumn 1Column 2
    Row 100
    Row 200
  2. Matrix B (n×p)
    Matrix B (n×p)
    Row / ColumnColumn 1Column 2
    Row 100
    Row 200
  3. Each entry is the dot product of a row of A with a column of B → A × B
    Each entry is the dot product of a row of A with a column of B → A × B
    Row / ColumnColumn 1Column 2
    Row 100
    Row 200

About Matrix Multiplication, Determinants & Inverses

Matrices are grids of numbers that represent linear transformations — rotations, scalings, projections — and the operations on them have geometric meaning. Matrix multiplication isn’t element-by-element: each entry of the product is the dot product of a row of the first matrix with a column of the second, which is why the inner dimensions must match (an m×n times an n×p gives an m×p) and why, unlike ordinary numbers, AB usually isn’t the same as BA.

The determinant of a square matrix is a single number that measures how much the transformation scales area or volume — and, crucially, whether it’s reversible: a determinant of zero means the transformation collapses space onto a lower dimension, so there’s no inverse. When the determinant is non-zero, the inverse matrix undoes the transformation, and this tool finds it by Gaussian elimination — augmenting the matrix with the identity and reducing until the original becomes the identity. To keep round-off error small it uses partial pivoting, and it snaps results that are a hair away from a whole number back to the integer — all while running entirely on your device.