Read the two statements and choose the correct option.

I. For $A = \begin{bmatrix}1 & 2 \\ 2 & 1\end{bmatrix}$ and $B = \begin{bmatrix}3 & 1 \\ 1 & 3\end{bmatrix}$, $AB = BA$.

II. $AB = BA$ for any two 2 × 2 matrices $A$ and $B$.

Explanation

1. 01

   I: $AB = \begin{bmatrix}5 & 7 \\ 7 & 5\end{bmatrix} = BA$. True.

2. 02

   II: false; for $\begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$ and $\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$ the two products differ. Matrix multiplication is not commutative in general.