If (3 5; 7 9) = X + Y, where X is skew-symmetric matrix and Y is symmetric matrix. Find |X|.

Let $A = \begin{pmatrix} 3 & 5 \\ 7 & 9 \end{pmatrix}$, so $A^T = \begin{pmatrix} 3 & 7 \\ 5 & 9 \end{pmatrix}$. $X = \frac{1}{2}(A - A^T) = \frac{1}{2}\begin{pmatrix} 0 & -2 \\ 2 & 0 \end{pmatrix} = \begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$ $|X| = 0 \times 0 - (-1)(1) = 1$