Find the determinant of A = [[4, 7], [2, 5]].

Step 1: Recall the determinant formula for a 2 × 2 matrix.

For A = [[a, b], [c, d]]:

det(A) = ad - bc

Step 2: Identify the entries.

a = 4
b = 7
c = 2
d = 5

Step 3: Substitute into the formula.

det(A) = (4)(5) - (7)(2)

Step 4: Multiply.

det(A) = 20 - 14

Step 5: Subtract.

det(A) = 6

Therefore, the determinant of A is 6.