Bonpoc: (} 1&2 -2&-1 ) Bblunclute npowsseperme Marput 1) (} 3&0 4&-1 ) 2) (} -1&2 -4&-1 )

To solve the matrix multiplication problem, we need to multiply the given matrices element-wise and sum the products for each position in the resulting matrix.<br /><br />Given matrices:<br />$A = \begin{pmatrix} 1 & 2 \\ -2 & -1 \end{pmatrix}$<br />$B = \begin{pmatrix} 3 & 0 \\ -2 & 1 \end{pmatrix}$<br /><br />The resulting matrix $C$ will be:<br />$C = A \cdot B = \begin{pmatrix} c_{11} & c_{12} \\ c_{21} & c_{22} \end{pmatrix}$<br /><br />To find each element of the resulting matrix, we use the formula:<br />$c_{ij} = \sum_{k=1}^{n} a_{ik} \cdot b_{kj}$<br /><br />Let's calculate each element:<br /><br />$c_{11} = (1 \cdot 3) + (2 \cdot -2) = 3 - 4 = -1$<br />$c_{12} = (1 \cdot 0) + (2 \cdot 1) = 0 + 2 = 2$<br />$c_{21} = (-2 \cdot 3) + (-1 \cdot -2) = -6 + 2 = -4$<br />$c_{22} = (-2 \cdot 0) + (-1 \cdot 1) = 0 - 1 = -1$<br /><br />So, the resulting matrix $C$ is:<br />$C = \begin{pmatrix} -1 & 2 \\ -4 & -1 \end{pmatrix}$<br /><br />Therefore, the correct answer is:<br />2) $(\begin{matrix} -1&2\\ -4&-1\end{matrix} )$