Evaluate the determinants:

We know that determinant of A is calculated as

Now,

= (x² – x + 1)(x + 1) - (x - 1)(x + 1)

= (x³ - x² + x + x² – x + 1) - (x² - 1)

= x³ + 1 - x² + 1

= x³ - x² + 2

Ans. The determinant of the above matrix is x³ - x² + 2.