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.

Step-by-step solution

Statement I: A non-singular matrix is a square matrix whose determinant is non-zero, i.e., |A| 0 . For any non-singular matrix, the inverse A⁻¹ always exists and is given by A⁻¹ = 1 |A| 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 ,