If A is a square matrix of order 3 and \(|A| = 4\), then the value of \(|2A^T|\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 32
Two standard results are used: for a matrix of order n, \(|kA| = k^n|A|\), and \(|A^T| = |A|\). Here n = 3 and k = 2:
\( |2A^T| = 2^3\,|A^T| \)
\( = 8\,|A| = 8 \times 4 = 32 \)
Tip: Multiplying a matrix of order n by k multiplies every row by k, so the determinant is multiplied by \(k^n\), not by k. Taking \(|2A^T| = 2|A| = 8\) is the usual slip.