Exercises: Understand Matrix Multiplication Properties

Work through each section in order. Show your work where indicated.

Grade 9·18 problems·~30 min·Common Core Math - HS Number and Quantity·standard·hsn-vm-c-9

Work through problems with immediate feedback

Recall / Warm-Up

For real numbers, $ab = ba$ for all $a, b$ . Is this true for matrices?

Yes — multiplication of matrices is always commutative.

No — matrix multiplication is generally NOT commutative; $AB \neq BA$ in most cases.

Yes — but only when the matrices are square.

No — but $AB = BA$ is true whenever both products are defined.