# Find the product of the matrices $\begin{bmatrix}2 &3&4\\-1&2&-5\end{bmatrix}$ and $\begin{bmatrix}1&2\\3&-4\\-5&6\end{bmatrix}$

(A) 0 (B) 15 (C) $\begin{bmatrix}-9&16\\80&-40\end{bmatrix}$ (D) $\begin{bmatrix}9&16\\80&40\end{bmatrix}$

Let the given matrices be denoted by $A$ and $B$ respectively.
$A$ is of the type $2\times 3$ and $B$ is of the type $3\times 2$
The product $AB$ is defined and is a matrix of the type $2\times 2$
$AB=\begin{bmatrix}-9&16\\80&-40\end{bmatrix}$
Hence (c) is the correct answer.