Q.If $A=\begin{pmatrix}1&2\\3&-1\end{pmatrix}$ and $B=\begin{pmatrix}0&-1\\2&4\end{pmatrix}$, find $2A-3B$.

An expression like $2A-3B$ is evaluated by scalar-multiplying each matrix first, then subtracting element-by-element.

Step 1 — Scalar multiply each matrix separately

Step 2 — Subtract element-by-element

$2A-3B = \begin{pmatrix}2-0&4-(-3)\\6-6&-2-12\end{pmatrix} = \begin{pmatrix}2&7\\0&-14\end{pmatrix}$ …

Combine the scalar multiplication and subtraction into a single per-entry formula $2a_{ij}-3b_{ij}$ and evaluate each of the four entries directly, without writing out $2A$ and $3B$ as se …

Subtracting $A-B$ first and THEN trying to apply the scalars afterward (which does not distribute correctly unless both matrices are scaled by the SAME number) — each matrix mus …