Question

If $A$ and $B$ are square matrices of order $3$ such that $det\text{ }A=1$ and $det\text{ }B=-1$ then $det\text{ (-10}\,\text{AB)}$ is equal to

• A. $10$
• B. $-10$
• C. $-1000$
• D. $1000$

Answer 1

Answer: (D)

$1000$

Answer 2

$\det \,\,A=1,$
$\det \,\,B=-1$
$\det \,(-10AB)={{(-10)}^{3}}\,\det \,(AB)$
$[\because \,\,\det \,(kA)\,={{k}^{n}}\,\det \,(A)]$
(here, $n=3$ ) $=-1000\,\det \,(A)\,\det \,(B)$
$=1+\log \,abc$