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Matrix Calculator

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Enter two matrices to add, subtract, multiply, transpose, or find the determinant - for 2×2 or 3×3 matrices.

Matrix Calculator

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Matrix A
Matrix B
Result

The operations

Addition/Subtraction: add or subtract matching positions Multiplication: row of A x column of B, summed, for each position Determinant (2x2): ad - bc Transpose: flip rows and columns
Example

Matrix A = [[1,2],[3,4]]: determinant = (1×4) - (2×3) = -2.

Step-by-step guide

  1. Choose 2×2 or 3×3.
  2. Enter the values for matrix A (and matrix B, if your chosen operation needs it).
  3. Choose the operation - the result updates instantly.

Why matrix multiplication isn't just multiplying matching positions

Unlike addition, matrix multiplication doesn't simply combine values in the same position - each entry in the result comes from multiplying an entire row of the first matrix by an entire column of the second, then summing those products. This is exactly why matrix multiplication generally isn't commutative (A×B usually doesn't equal B×A), unlike ordinary number multiplication, and why the number of columns in A must match the number of rows in B for the operation to even be defined (though this calculator keeps both matrices the same square size for simplicity).

Common mistakes

Assuming A×B equals B×A - matrix multiplication is generally not commutative, so the order genuinely matters.
Multiplying matching positions together (like regular elementwise multiplication) instead of the proper row-by-column method - this is a very common conceptual mix-up when first learning matrices.

Frequently asked questions

What does a determinant of zero mean?

It means the matrix is "singular" - it has no inverse, and represents a transformation that collapses space into a lower dimension (like squashing a 2D plane into a line).

What's a practical use for matrix transpose?

Transposing shows up constantly in statistics, computer graphics, and machine learning - for example, converting data between "rows as samples" and "columns as samples" formats, or as a step in more advanced matrix operations.

Does this support matrices larger than 3x3?

Not currently - this covers 2x2 and 3x3, which matches the vast majority of introductory linear algebra coursework and everyday use cases.

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