 Hello and welcome to the session. I am there to help you with the following problem. Let us see the problem. Evaluate the determinant x square minus x plus 1, x minus 1, x plus 1, x plus 1. Before writing the solution, let us see the key idea. Determinant of A is denoted by mod of A or determinant of 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 these square matrix. A is equal to A1B1A2B2. That's determinant A is equal to mod of A is equal to A1B2 minus A2B1. Now let us write the solution. We have x square minus x plus 1, x minus 1, x plus 1, and x plus 1 as our determinant. Now solving this using the key idea, we get x square minus 1, x square minus x plus 1 multiplied by x plus 1 minus x plus 1 multiplied by x minus 1, which is equal to x cube plus x square minus x square minus x plus x plus 1 minus x square minus 1, which is equal to this gets cancels. And this also gets canceled, so we are left with x cube plus 1. Now opening the brackets, we get minus x square plus 1, which is equal to x cube minus x square plus 2. Hence the required answer is q minus x square plus 2. I hope you understood the problem. Bye, and have a nice day.