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Algebra

Matrices, Determinants

jee_main_2026_april_4_shift_2

Grade 12

Question:

If A = [[1, 2], [3, 4]], and det(A) = d, and the determinant of A^2 is D, find D - d.

A. 2

B. 4

C. 6

D. 8

Step-by-Step Solution

Key Concept: Use det(A^2) = (det A)^2 and det(A) = ad - bc.

Step 1: det(A) = 1×4 - 2×3 = 4 - 6 = -2. So d = -2. Step 2: det(A^2) = (det A)^2 = (-2)^2 = 4. So D = 4. Step 3: D - d = 4 - (-2) = 6.

Correct Answer: C

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