ACT Math: Matrix Multiplication A(2x2) and B(2x3), Entry c23 and Dimensions

Exact Question Scenario

Matrix $A = \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}$ and Matrix $B = \begin{bmatrix} 2 & 0 & -3 \\ -1 & 5 & 2 \end{bmatrix}$. If matrix $C = AB$, what is the entry in row 2, column 3 ($c_{23}$)?

Step-by-Step Solution

1. Check Dimensions: $(2 \times 2) \cdot (2 \times 3) \implies \text{Product is } \mathbf{2 \times 3}$.
2. Compute $c_{23}$ (Row 2 of $A \times$ Col 3 of $B$):

$$ c_{23} = (1)(-3) + (4)(2) = -3 + 8 = \mathbf{5} $$