If matrix multiplication still feels mechanical or unclear, this book is for you. Build real intuition with 950+ fill-in-the-blank exercises designed for pencil-and-paper practice. Master shapes, identity, scaling, chaining, transpose, inverse, and tiled algorithms used in AI, machine learning, and data science.

Book Description

“What we should do is learn kind of basic things in mathematics, in modeling, mathematics that can be connected with reality”.

Yann LeCun, on The Information Bottleneck Podcast

Most people learn matrix multiplication by memorizing rules and procedures. They can follow the steps, but they don’t really see what’s happening especially when the shapes change or the multiplication chains get longer.

When I began teaching, I realised many students were stuck. They could compute, but they didn’t feel confident. This workbook is a product of that experience.

The emphasis here is on doing, not memorizing. You won’t read long proofs. Instead, you’ll fill in carefully designed blanks step by step, reasoning about shapes, rows, columns, and structure as you go. You’ll fill in missing dimensions, intermediate steps, and partial results not just final answers.

The goal isn’t just to get answers. It’s to build intuition you can trust, so you can catch mistakes earlier and know what a product should look like before you finish it.

By the end of this workbook, matrix multiplication should no longer feel fragile. This is not a reference book. It’s meant to be written in. Use a pencil. Work slowly. Make mistakes. That’s how you learn.

Key Features

• You work by hand ✍️, with real numbers
• You fill in the blanks instead of reading proofs
• You reason about shapes, rows, columns, and structure step by step
• You discover the math yourself, rather than being told the rules upfront

What you will learn

• Multiply matrices confidently using correct shapes and rules
• Recognize identity matrices, scaling, shifting, and their effects
• Understand why matrix multiplication is not commutative
• Apply associativity and distributive properties to simplify work
• Use chaining and transpose concepts in real computations
• Build intuition for inverse matrices and linear equations
• Strengthen speed and accuracy through progressive practice sets
• Learn tiled multiplication ideas for efficient computation

Who this book is for

This book is ideal for:

• Students learning linear algebra, machine learning, or AI
• Engineers and practitioners who “use” matrices but want deeper intuition
• Educators looking for a concrete, classroom-friendly teaching tool
• Anyone who has learned the rules—but never felt fully confident using them

This is not a reference book and not a collection of proofs. It’s a workbook designed to be written in.

Use a pencil. Solve by hand. Make mistakes. Slow down. Learn!

Table of Contents

1. Calculate
2. Complexity
3. Shape
4. Identity
5. Scale
6. Shift
7. Combine Rows
8. Combine Columns
9. Not Commutative
10. Associative
11. Distributive
12. Chain
13. Transpose
14. Inverse
15. Linear Equations
16. Tiled Algorithm