2×2 Matrix Multiplication

= +

Tap a term to see what it means, or .

Calculate

Example: A stretches the x axis to double, and B rotates the plane 90° anticlockwise. What does AB do — rotate and then stretch? And BA? Change the matrices to work out your own case.

Matrix A Two rows separated by a semicolon. Matrix B Two rows separated by a semicolon.

Step by step

What each term means

Entry of the Product ((AB)ᵢⱼ): The entry in row i and column j of AB. There are four, one for each pairing of a row of A with a column of B.
First Pair: The first entry of row i of A times the first of column j of B.
Second Pair: The second times the second. Adding the two pairs is the dot product of the row and the column.