Let and . Which of the following statements is…

MATHEMATICS · Single correct · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Let A=[0100]A = \begin{bmatrix}0 & 1 \\ 0 & 0\end{bmatrix} and B=[0010]B = \begin{bmatrix}0 & 0 \\ 1 & 0\end{bmatrix}. Which of the following statements is true? (a) AB=BA=OAB = BA = O (b) AB≠BAAB \neq BA and both ABAB and BABA are non-zero\text{non-zero} (c) AB=BA≠OAB = BA \neq O (d) AB≠O but BA=OAB \neq O \text{ but } BA = O

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