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

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Fluency Practice

Matrix $A$ is $2 \times 3$ and $B$ is $3 \times 4$ . Is $BA$ defined?

Yes — matrix multiplication is always defined for any two matrices.

Yes — because $AB$ is defined, $BA$ is too.

No — $B$ is $3 \times 4$ and $A$ is $2 \times 3$ . The inner dimensions are $4$ and $2$ , which don't match.

Yes — both $AB$ and $BA$ are always defined for the same pair of matrices.