Let $X_n \xrightarrow{d} X$ and $Y_n \xrightarrow{d} c$ where $c$ is a deterministic constant. Then as $n \to \infty$: (a) $Y_n \xrightarrow{\mathbb{P}} c$. (b) $X_n + Y_n \xrightarrow{d} X + c$. (c) In the scalar case ($k = 1$): $X_n Y_n \xrightarrow{d} cX$, and if $c \neq 0$ then $X_n/Y_n \xrightarrow{d} X/c$. (d) If $(A_n)_{n \geq 0}$ are random matrices with $(A_n)_{ij} \xrightarrow{\mathbb{P}} A_{ij}$ for each $(i,j)$, where $A$ is deterministic, then $A_n X_n \xrightarrow{d} AX$.