Multiplication of Matrices Exercise with Solution

\[
\textbf{Exercise: Multiplication of Matrices}
\]

\[
\textbf{Q1: Multiply the Square Matrices A and B, where:}
\]
\[
A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}
\] Solution

\[
\textbf{Q2: Multiply the Diagonal Matrices A and B, where:}
\]
\[
A = \begin{pmatrix} 3 & 0 \\ 0 & 5 \end{pmatrix}, \quad B = \begin{pmatrix} 2 & 0 \\ 0 & 4 \end{pmatrix}
\] Solution

\[
\textbf{Q3: Multiply the Scalar Matrices A and B, where:}
\]
\[
A = \begin{pmatrix} 2 & 0 \\ 0 & 2 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}
\] Solution

\[
\textbf{Q4: Multiply the Identity Matrices A and B, where:}
\]
\[
A = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}
\] Solution

\[
\textbf{Q5: Multiply the Zero Matrices A and B, where:}
\]

\[
A = \begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}
\]

\[
A = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}
\]  Solution

\[
\textbf{Q6: Multiply the Symmetric Matrix A by the Skew-Symmetric Matrix B, where:}
\]

\[
A = \begin{pmatrix} 2 & 1 \\ 1 & 3 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}
\] Solution

\[
\textbf{Q7: Multiply Matrix A (2×3) by Matrix B (3×2), where:}
\]
\[
A = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix}, \quad B = \begin{pmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{pmatrix}
\] Solution

\[
\textbf{Q8: Multiply Matrix A (3×2) by Matrix B (2×4), where:}
\]
\[
A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{pmatrix}, \quad B = \begin{pmatrix} 7 & 8 & 9 & 10 \\ 11 & 12 & 13 & 14 \end{pmatrix}
\] Solution

\[
\textbf{Q9: Multiply Matrix A (1×3) by Matrix B (3×1), where:}
\]
\[
A = \begin{pmatrix} 2 & 4 & 6 \end{pmatrix}, \quad B = \begin{pmatrix} 1 \\ 3 \\ 5 \end{pmatrix}
\] Solution

\[
\textbf{Q10: Multiply Matrix A (3×3) by Matrix B (3×2), where:}
\]
\[
A = \begin{pmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \\ 2 & 2 & 0 \end{pmatrix}, \quad B = \begin{pmatrix} 3 & 1 \\ 2 & 4 \\ 1 & 0 \end{pmatrix}
\] Solution