Matrix Multiplication Workbook: Fill-in-the-Blank Puzzles to Build Real Intuition by Hand

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 PodcastMost 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 FeaturesYou work by hand ✍️, with real numbersYou fill in the blanks instead of reading proofsYou reason about shapes, rows, columns, and structure step by stepYou discover the math yourself, rather than being told the rules upfrontWhat you will learnMultiply matrices confidently using correct shapes and rulesRecognize identity matrices, scaling, shifting, and their effectsUnderstand why matrix multiplication is not commutativeApply associativity and distributive properties to simplify workUse chaining and transpose concepts in real computationsBuild intuition for inverse matrices and linear equationsStrengthen speed and accuracy through progressive practice setsLearn tiled multiplication ideas for efficient computationWho this book is forThis book is ideal for:Students learning linear algebra, machine learning, or AIEngineers and practitioners who “use” matrices but want deeper intuitionEducators looking for a concrete, classroom-friendly teaching toolAnyone who has learned the rules—but never felt fully confident using themThis 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 ContentsCalculateComplexityShapeIdentityScaleShiftCombine RowsCombine ColumnsNot CommutativeAssociativeDistributiveChainTransposeInverseLinear EquationsTiled Algorithm Read more