Question

If $A$ is a square matrix of order $3$ and a is a real number, then determinant $|\alpha \,\,\,A|$ is equal to

• A. ${{\alpha }^{2}}\,|\,\,A|$
• B. $\alpha \,|\,\,A|$
• C. ${{\alpha }^{3}}\,|\,\,A|$
• D. None of these

Answer 1

Answer: (C)

${{\alpha }^{3}}\,|\,\,A|$

Answer 2

Order of square matrix A is 3 and $a\in R.$
Then, $|\alpha \,A{{|}_{3\times 3}}={{\alpha }^{3}}|A{{|}_{3\times 3}}$