Step 1: Identify the elements of the matrix H. H = [[2, 3], [4, 5]] means that the first row has 2 and 3, and the second row has 4 and 5.
Step 2: Use the formula for the determinant of a 2x2 matrix, which is det(H) = (a*d) - (b*c), where a, b, c, and d are the elements of the matrix. Here, a = 2, b = 3, c = 4, and d = 5.
Step 3: Substitute the values into the formula: det(H) = (2*5) - (3*4).
Step 4: Calculate the first part: 2*5 = 10.
Step 5: Calculate the second part: 3*4 = 12.
Step 6: Subtract the second part from the first part: 10 - 12 = -2.
