What is the determinant of the square matrix A(x) [(2x+1) -2] [(2x+1) (2x-1)] ?

Since the given matrix is a square matrix, we may evaluate
it's determinant.

Det A = a11*a22 -
a12*a21

The determinant is the difference between the
product of the terms located on the first diagonal (1st term from the 1st row* the 2nd
term from the 2nd row) and the product of the terms located on the 2nd diagonal (2nd
term from the 1st row *the 1st term from the 2nd row)

Let's
identify the terms: a11 = (2x+1) ; a12 = (-2) ; a21 = (2x+1) and a22 =
(2x-1).

Det A(x) = (2x+1)*(2x-1) -
(-2)*(2x+1)

Det A = (2x+1)*(2x - 1 +
2)

Det A = (2x+1)*(2x + 1)

Det
A = (2x+1)^2

The requested determinant of the
square matrix A(x) is Det A = (2x+1)^2.