Divide the Symmetric Matrix A = [(4, 2), (2, 4)] by the Skew-Symmetric Matrix B = [(0, 1), (-1, 0)].

[latex] \[ \textbf{Divide the Symmetric Matrix A by the Skew-Symmetric Matrix B, where:} \] \[ A = \begin{pmatrix} 4 & 2 \\ 2 & 4 \end{pmatrix}, \quad B = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} \] \[ \textbf{Solution: Find the inverse of B, then multiply A by B^{-1}.} \] \[ \text{Step 1: Compute the determinant of B.} \] \[ \text{det}(B) = (0)(0) – (1)(-1) = 0 – (-1) = 1 \] \[ \text{Step 2: Compute the inverse of B.} \] \[ B^{-1} = \frac{1}{\text{det}(B)} \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \] \[ \text{Step 3: Multiply A by B^{-1}.} \] \[ A \div B = A \cdot B^{-1} = \begin{pmatrix} 4 & 2 \\ 2 & 4 \end{pmatrix} \cdot \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix} \] \[ A \div B = \begin{pmatrix} (4)(0) + (2)(1) & (4)(-1) + (2)(0) \\ (2)(0) + (4)(1) & (2)(-1) + (4)(0) \end{pmatrix} \] \[ A \div B = \begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix} \] \[ \textbf{Answer: } \begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix} \]