Overview
A matrix is an array of numbers arranged in rows and columns. Two matrices of the same size can be added or subtracted entry by entry. Multiplication requires the first matrix's column count to equal the second's row count; here both matrices are 2×2.
Formula
For multiplication: (AB)ᵢⱼ = Aᵢ₁B₁ⱼ + Aᵢ₂B₂ⱼ. The determinant is ad − bc.
How it works
Enter the entries of A
Ordered by row, then column.
Enter the entries of B
Using the same order.
Choose the operation
Addition, subtraction or multiplication.
Read the result
The four entries, determinant and trace appear.
Worked examples
Example 1: addition
A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]], giving [[6, 8], [10, 12]].
Example 2: multiplication
With the same matrices, the result is [[19, 22], [43, 50]].
Frequently asked questions
Is matrix multiplication commutative?
No. AB usually differs from BA.
What is the trace?
The sum of the main diagonal entries, A₁₁ + A₂₂.
When is a matrix invertible?
When its determinant is nonzero.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.