1. **Problem statement:** Given matrices $A = \begin{pmatrix} 2 & -3 \\ \end{pmatrix}$ and $B = \begin{pmatrix} 1 & 0 \\ -3 & \end{pmatrix}$, calculate $AB$. 2. **Matrix multiplication formula:** For matrices $A$ of size $m \times n$ and $B$ of size $n \times p$, the product $AB$ is an $m \times p$ matrix where each element is computed as: $$ (AB)_{ij} = \sum_{k=1}^n A_{ik} B_{kj} $$ 3. **Check dimensions:** Here, $A$ is 1x2 and $B$ is 2x1 (assuming from given entries), so multiplication is possible and result is 1x1. 4. **Calculate $AB$:** $$ AB = \begin{pmatrix} 2 & -3 \end{pmatrix} \times \begin{pmatrix} 1 \\ -3 \end{pmatrix} = \begin{pmatrix} 2 \times 1 + (-3) \times (-3) \end{pmatrix} = \begin{pmatrix} 2 + 9 \end{pmatrix} = \begin{pmatrix} 11 \end{pmatrix} $$ 5. **Final answer:** $AB = \begin{pmatrix} 11 \end{pmatrix}$. This completes the first problem as per instructions.