Q.If $A=\begin{pmatrix}4&-2\\2&6\end{pmatrix}$ and $B=\begin{pmatrix}-2&6\\4&-2\end{pmatrix}$, find the matrix $X$ such that $2X=A+B$.

Finding $A+B$ first, and then dividing every element of the sum by 2, gives $X$.

Step 1 — Find $A+B$

Step 2 — Solve $2X=A+B$ for $X$

Since $2X=\begin{pmatrix}2&4\\6&4\end{pmatrix}$, dividing every element by 2 (equivalently, scalar-multiplying by $\tfrac12$) gives

$X = \begin{pmatrix}1&2\\3&2\end{pmatrix}$ …

Forgetting to divide EVERY element of $A+B$ by 2 (e.g. dividing only the first entry), or dividing $A$ and $B$ by 2 separately before adding instead of adding first — both give a w …