Question

If |A| denotes the value of the determinant of the square matrix A of order 3, then $| - 2A| =$

• A. $- 8|A|$
• B. $8|A|$
• C. $- 2|A|$
• D. None of these

Answer 1

Answer: (A)

$- 8|A|$

Answer 2

We know that, det. $( - A) = ( - 1)^{n}\det A$, where n is order of square matrix

If A is square matrix of order 3, Then $n = 3$. Hence

$| - 2A| = ( - 2)^{3}|A| = - 8|A|$.