Consider the following statements:
Statement I: If A is a non-singular matrix, then \(A^{-1}\) exists.
Statement II: If A and B are symmetric matrices of same order, then \((AB - BA)\) is a skew symmetric matrix.
Choose the correct option.

Statement I:
A non-singular matrix is a square matrix whose determinant is non-zero, i.e., \(|A| \neq 0\).
For any non-singular matrix, the inverse \(A^{-1}\) always exists and is given by \(A^{-1} = \dfrac{1}{|A|} \text{adj}(A)\).
Thus, Statement I is true.

Statement II:
Given \(A\) and \(B\) are symmetric matrices of the same order, we have \(A^T = A\) and \(B^T = B\).
Let \(P = AB - BA\).
Taking the transpose of \(P\):
\(P^T = (AB - BA)^T\)
\(P^T = (AB)^T - (BA)^T\)
\(P^T = B^T A^T - A^T B^T\)
Substituting \(A^T = A\) and \(B^T = B\):
\(P^T = BA - AB\)
\(P^T = -(AB - BA) = -P\)
Since \(P^T = -P\), the matrix \((AB - BA)\) is a skew-symmetric matrix.
Thus, Statement II is true.

Both Statement I and Statement II are true.

Answer: Statement I is true and Statement II is true