Math

Matrix Calculator

Add, subtract, multiply matrices and find determinants.

🔢

Matrix Calculator

Operation

Results

How to Use Matrix Calculator

1 Select the matrix operation
2 Enter values for Matrix A (and Matrix B if required)
3 Click Calculate to get the result matrix

Formula & Methodology

Matrix Addition: Add corresponding elements
Matrix Multiplication: Each element = dot product of row × column
Determinant 2×2: |A| = ad - bc
Transpose: Rows become columns

About Matrix Calculator

Our matrix calculator handles the most common matrix operations. Matrices are fundamental in linear algebra, used in computer graphics, machine learning, physics, and engineering.

Frequently Asked Questions

A matrix is a rectangular array of numbers arranged in rows and columns. An m×n matrix has m rows and n columns. Matrices are used in linear algebra, computer graphics, statistics, and many engineering fields.

Matrix multiplication requires the number of columns in the first matrix to equal the number of rows in the second. Each element c(i,j) = sum of a(i,k) × b(k,j) for all k. The result is an m×p matrix when multiplying m×n by n×p.

The determinant is a scalar value that can be computed from the elements of a square matrix. For a 2×2 matrix [[a,b],[c,d]], det = ad − bc. A non-zero determinant means the matrix is invertible.

The inverse A⁻¹ of matrix A satisfies A × A⁻¹ = I (identity matrix). It only exists if det(A) ≠ 0. For a 2×2 matrix, the inverse swaps the diagonal elements and negates the off-diagonal ones, then divides by the determinant.

Transposing a matrix flips it over its diagonal — rows become columns and columns become rows. The transpose of an m×n matrix is an n×m matrix. Notation: A^T or A'.

Two matrices can only be added or subtracted if they have the same dimensions (same number of rows and columns). You simply add or subtract corresponding elements.

Matrices are used in 3D computer graphics (transformations, rotations), solving systems of linear equations, machine learning (neural network weights), image processing, cryptography, and structural engineering analysis.

Found this useful? Share it!

Share: Twitter Facebook WhatsApp