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 textAB) is equal to

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 textAB) is equal to (A)  10  (B)  -10  (C)  -1000  (D)  1000

Tardigrade Admin · Accepted Answer

det A=1, det B=-1 det (-10AB)=(-10)3 det (AB) [∵ det (kA) =kn det (A)] (here, n=3 ) =-1000 det (A) det (B) =1+ log abc

Q. If $A$ and $B$ are square matrices of order $3$ such that $d e t A = 1$ and $d e t B = - 1$ then $d e t (-10 AB)$ is equal to

$10$

$- 10$

$- 1000$

$1000$

$det A = 1,$
$det B = - 1$
$det (- 10 A B) = (- 10)^{3} det (A B)$
$[∵ det (k A) = k^{n} det (A)]$
(here, $n = 3$ ) $= - 1000 det (A) det (B)$
$= 1 + lo g ab c$

Q. If A and B are square matrices of order 3 such that detA=1 and detB=−1 then det (-10AB) is equal to

10

−10

−1000

1000