Let \(\mathrm{A}, \mathrm{B}\) be two \(3 \times 3\) matrices and \(\mathrm{C}\) be a \(3 \times 3\) unit matrix such that \(A B-C\) is a non-singular matrix. Let \(\mathrm{D}=(\mathrm{AB}-\mathrm{C})^{-1}\). Then, consider the following statements.
Statement I : \(\operatorname{det}(\mathrm{BA})=\operatorname{det}(\mathrm{BA}-\mathrm{C}) \operatorname{det}(\mathrm{BDA})\)
Statement II : ABD = DAB
Which of the above statements is (are) true?

1. A Statement I is true, but Statement II is false
2. B Statement II is true, but Statement I is false
3. C Both Statement I and Statement II are true
4. D Both Statement I and Statement II are false