Handitab

Matrix Calculator

Add, subtract, and multiply matrices, and find the determinant, inverse, transpose, and rank of a matrix typed one row per line.

About Matrix Calculator

A matrix is a rectangular grid of numbers. This calculator adds and subtracts matrices of equal size, multiplies them when the columns of A equal the rows of B, and transposes by swapping rows with columns. Determinant, inverse, and rank are found by Gaussian elimination with partial pivoting. The inverse exists only for a square matrix whose determinant is not zero. Results are rounded to six decimal places.

How to use Matrix Calculator

  1. Type or paste into the "Matrix A (one row per line)" box and the "Matrix B (used for A + B, A − B, and A × B)" box, or press "Use example" to try it with sample data.
  2. Set "Operation" if the defaults do not fit.
  3. The result appears below and updates as you type.
  4. Copy the result with the copy button, or download it as a file where that is offered.

Questions about Matrix Calculator

Why can some matrices not be inverted?

A square matrix has no inverse when its determinant is zero. That happens when one row or column is a combination of the others, so the matrix squashes space into a lower dimension and the operation cannot be undone.

Is matrix multiplication commutative?

No. In general A × B is not equal to B × A, and one product may exist while the other does not. The number of columns in the left matrix must equal the number of rows in the right one.

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