If A is a square matrix of order 3 and det(A) = 1. If B = 2A is another matrix, the value of det(B) is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 8
Multiplying a matrix by k multiplies every row by k, and each row brings out a factor k from the determinant. For a matrix of order n:
\(|kA| = k^n\,|A|\)
Here n = 3 and k = 2:
\(\det(B) = |2A| = 2^3 \times 1 = 8\)
Tip: |kA| = kn|A|, not k|A|; writing 2 × 1 = 2 is the usual trap.