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.
8
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.