If A is a square matrix of order 4 and |A| = 4, then |2A| will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 64
Multiplying A by k multiplies every row by k, and each row brings out a factor k from the determinant. For a square matrix of order n this gives the scalar multiple result \(|kA| = k^n|A|\). Here n = 4 and k = 2:
\(|2A| = 2^4|A|\)
\(= 16 \times 4 = 64\)
Why the other options are incorrect
Option (1) 8 — Incorrect. This is 2|A|; the factor 2 comes out of each of the 4 rows, not just once.
Option (3) 16 — Incorrect. This is \(2^2|A|\), the value for a matrix of order 2.
Option (4) 4 — Incorrect. This is |A| itself; doubling the matrix changes the determinant.