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Matrix Multiplication

Matrix multiplication is the operation that surprises people: it is not done entry by entry, the product is not always defined, and AB is usually not the same as BA.

This quiz walks through the dimension rule, the row-by-column mechanics, individual entries of a product, squaring a matrix, and the properties that do and do not carry over from ordinary numbers.

If multiplication is the step where matrices stopped making sense, this is the quiz to take.

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What This Quiz Covers

  • When the product AB is defined
  • Dimensions of the resulting matrix
  • Computing a product row by column
  • Finding a single entry of a product
  • Why AB and BA differ
  • The identity matrix and powers of a matrix
Sample questions3 of 13 shown
Q1
When is the product AB defined?
Q2
A is 4×3 and B is 3×5. What are the dimensions of AB?
Q3
A is 2×3 and B is 2×3. What can be said about AB?
Answer all 13 questions on Cletica →

The matrices series

Matrices Basics
Rows, columns, determinants — the grid of numbers behind linear algebra.
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Matrix Addition and Scalar Multiplication
Adding, subtracting and scaling matrices — the first operations after the basics.
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Determinants of 2×2 and 3×3 Matrices
Computing determinants and reading what they tell you about a matrix.
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The Inverse of a 2×2 Matrix
When a 2×2 matrix can be inverted, how to do it, and how to check the result.
Hard
Solving Systems of Equations with Matrices
Writing a linear system as a matrix equation and solving it.
Hard

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