Matrices & Determinants
Properties of determinants
Grade Class 12

Question:

Let p and p + 2 be prime numbers and let Δ = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
(A) 2
(B) 4
(C) 24
(D) 36

Step-by-Step Solution

Key Concept: Use properties of determinants to factor out common terms from rows and columns. Specifically, factor out p!, (p+1)!, and (p+2)! from the rows, then simplify the resulting 3x3 determinant.
Factor out p! from R1, (p+1)! from R2, and (p+2)! from R3. Then factor out p! from C1, (p+1)! from C2, and (p+2)! from C3. The determinant simplifies to a constant value multiplied by powers of p and (p+2).
Correct Answer: 2

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