Matrix Calculator

Add, subtract, multiply matrices and find transpose, determinant, and inverse.

Interactive Calculator Coming Soon

The interactive version of this calculator is under development. In the meantime, you can use the formula and worked examples below to calculate manually.

Scroll down to see the formula, step-by-step explanation, and FAQs.

Matrix Calculator Formula & How It Works

(AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ | det(A) = ad−bc (2×2) | A⁻¹ = (1/det) × adj(A)
  • Matrix addition: element-wise (same dimensions required)
  • Multiplication: rows × columns (A must be m×n, B must be n×p)
  • Determinant (2×2): ad−bc
  • Inverse: exists only if det(A) ≠ 0 (non-singular matrix)

Matrix operations are fundamental to linear algebra, computer graphics, machine learning, and physics. Addition/subtraction: element-wise (same dimensions). Multiplication: dot product of rows with columns (inner dimensions must match). The determinant measures the 'scale factor' of a linear transformation; zero determinant means the matrix is not invertible.

Matrix Calculator FAQs

What is matrix multiplication?

To multiply matrix A(m×n) by B(n×p): result C(m×p) where Cᵢⱼ = row i of A · column j of B (dot product). Order matters: AB ≠ BA in general. Both n (A's columns) must match n (B's rows).

What is a determinant used for?

The determinant tells you if a matrix is invertible (det ≠ 0), the area/volume scaling factor of a linear transformation, whether a system of equations has a unique solution (Cramer's rule), and in eigenvalue calculations.

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