If matrix A and matrix B, what is (AB)'?

Question 80

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If $A = \begin{bmatrix}2 \\ -1\end{bmatrix}$ and $B = \begin{bmatrix}3 & 1\end{bmatrix}$ , what is $(AB)'$ ?

\begin{bmatrix}6 & 2 \\ -3 & -1\end{bmatrix}

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\begin{bmatrix}5\end{bmatrix}

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\begin{bmatrix}6 & -3 \\ 2 & -1\end{bmatrix}

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\begin{bmatrix}6 & -1 \\ 2 & -3\end{bmatrix}

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CorrectNot quiteAnswer C

Correct answer: C

$AB = \begin{bmatrix}6 & 2 \\ -3 & -1\end{bmatrix}$ , a 2 × 2 matrix.
Its transpose is $\begin{bmatrix}6 & -3 \\ 2 & -1\end{bmatrix}$ , which is $B'A'$ , as the reversal law says.

Worth noting

$\begin{bmatrix}5\end{bmatrix}$ is $A'B'$ , a 1 × 1 matrix: the order of the transposes was not reversed.

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