 Hello and welcome to the session. Let us understand the following problems today. Evaluate the determinant cos theta minus sin theta sin theta cos theta. Before writing the solution, let us understand the key idea. Determinant of A is denoted by mod of A or determinant A or delta. Consider a system of linear equations A1x plus B1y is equal to C1 and A2x plus B2y is equal to C2 which is associated with the square matrix A which is equal to A1B1 A2B2 thus determinant is equal to mod of A is equal to A1B2 minus A2B1. Now, let us write the solution. We have cos theta minus sin theta sin theta cos theta as our determinant. Now using the key idea we solve this which is equal to cos theta into cos theta minus sin theta multiplied by minus sin theta which is equal to cos square theta plus sin square theta which is equal to 1. Therefore, the required answer is 1. I hope you understood the problem Bye and have a nice day.