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Math • Matrix Multiplication Calculator (A × B)

Matrix Multiplication Calculator (A × B)

Multiply two 2×2 matrices A × B and get the resulting product matrix, step by step.

Matrix A (2×2)
×
Matrix B (2×2)
=
Product C = A × B
19
22
43
50
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Calculation Guide & Reference

2×2 Matrix Multiplication Mathematics

Matrix multiplication calculator multiplies two 2×2 matrices A × B and returns the resulting product matrix.

Standardized Mathematical Formula
(A×B)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ

Each entry in the product matrix is the dot product of a row from the first matrix and a column from the second — row 1 of A combines with column 1 of B for entry (1,1), row 1 of A with column 2 of B for entry (1,2), and so on.

Variables:
A, B:The two 2×2 matrices being multiplied, in order A × B
(A×B)ᵢⱼ:The entry in row i, column j of the product matrix
How It Works (Step-by-Step)
  • 1Enter the four entries of matrix A and the four entries of matrix B.
  • 2View the resulting 2×2 product matrix A × B.
Real-World Numerical Example
A = [[1,2],[3,4]] × B = [[5,6],[7,8]]

Multiply matrix A = [[1,2],[3,4]] by matrix B = [[5,6],[7,8]].

•Entry (1,1): (1×5) + (2×7) = 5 + 14 = 19.
•Entry (1,2): (1×6) + (2×8) = 6 + 16 = 22.
•Entry (2,1): (3×5) + (4×7) = 15 + 28 = 43.
•Entry (2,2): (3×6) + (4×8) = 18 + 32 = 50.
Result: The product matrix A × B = [[19, 22], [43, 50]].
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

No — in general A × B ≠ B × A for matrices, even when both products are defined. Order matters, unlike multiplying ordinary numbers.

No — the number of columns in the first matrix must equal the number of rows in the second matrix. Two 2×2 matrices always satisfy this, which is why they're a common starting example.

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