How does the Matrix Calculator work?

Matrix addition/subtraction: add corresponding elements (matrices must be same size) Then: Matrix multiplication: row × column dot products (A must have same columns as B has rows) Then: Determinant (2×2): det(A) = ad − bc for [[a,b],[c,d]] Then: Transpose: flip rows and columns (rows become columns).

Can you give an example of how to use the Matrix Calculator?

Example: Input det([[3,8],[4,6]]) gives a result of −14 (3×6 − 8×4 = 18−32 = −14).

Is the Matrix Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Matrix Calculator?

Our Matrix Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

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Matrix Calculator

Matrix Calculator (2×2)

Matrix A

Matrix B

A matrix is a rectangular array of numbers arranged in rows and columns. Matrices are fundamental in linear algebra, used for solving systems of equations, 3D computer graphics, machine learning (neural networks), quantum mechanics, and engineering.

Operation	Requirement	Result Size
Addition (A+B)	Same dimensions	Same as A and B
Multiplication (AB)	A cols = B rows	m×p if A is m×n, B is n×p
Transpose (Aᵀ)	Any matrix	n×m if A is m×n
Determinant	Square matrix only	Scalar
Inverse (A⁻¹)	Square, det ≠ 0	Same as A

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Pro Tip

Matrix multiplication is NOT commutative: AB ≠ BA in general. Always check the order matters for your application.

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Did You Know?

The word "matrix" was coined by mathematician James Joseph Sylvester in 1850. In 3D computer graphics, every rotation, scaling, and translation of objects on your screen is performed using matrix multiplication.

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Matrix Calculator

Matrix Calculator (2×2)

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Matrix Calculator (2×2)