Matrix Operations

Add, subtract, multiply, transpose and row-reduce matrices, with every entry’s calculation shown. Try “multiply [[1,2],[3,4]] by [[0,1],[1,0]]”.

Try an example:

How the Matrix Operations works

  1. Check the dimensions allow the operation (columns of A = rows of B to multiply).
  2. Each entry of AB is the dot product of a row of A with a column of B.
  3. Write out the result matrix and double-check one entry.

Frequently asked questions

Is matrix multiplication commutative?

No. In general AB ≠ BA, so order matters.

When can two matrices be multiplied?

When the number of columns in the first equals the number of rows in the second.

More Matrices & Linear Algebra calculators

Determinant & Inverse2x2 and 3x3 determinants, inverse matrices, Cramer's rule. Eigenvalues & EigenvectorsCharacteristic polynomial and eigenpairs.

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