Given two matrices A and B, where $$A = \begin{bmatrix} -1 & 2 \end{bmatrix}$$ and $$B = \begin{bmatrix} 3 \\ 4 \end{bmatrix}$$, then product AB is :

Given,

Matrix A is of order 1 × 2 and matrix B is of order 2 × 1.

We know that,

If matrix A is of order $m \times n$ and matrix B is of order $n \times p$, then the order of the product AB is $m \times p$.

∴ Order of AB = 1 × 1

Calculating,

$$\Rightarrow AB = \begin{bmatrix*}[r] -1 & 2 \end{bmatrix*}\begin{bmatrix*}[r] 3 \\ 4 \end{bmatrix*} \\[1em] = \begin{bmatrix*}[r] -1 \times 3 + 2 \times 4 \end{bmatrix*} \\[1em] = \begin{bmatrix*}[r] -3 + 8 \end{bmatrix*} \\[1em] = \begin{bmatrix*}[r] 5 \end{bmatrix*}.$$

Hence, option 3 is the correct option.