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

Let $A = \begin{bmatrix}1&2\\0&1\end{bmatrix}$ and $B = \begin{bmatrix}1&0\\1&1\end{bmatrix}$ . Compute $AB$ and $BA$ . Which statement is true?

$AB = BA = \begin{bmatrix}3&2\\1&1\end{bmatrix}$

$AB = \begin{bmatrix}3&2\\1&1\end{bmatrix}$ and $BA = \begin{bmatrix}1&2\\1&3\end{bmatrix}$ ; they are different.

$AB = BA = \begin{bmatrix}1&2\\1&3\end{bmatrix}$

$AB$ is defined but $BA$ is undefined for these matrices.