If A and B are square matrices of order 3 such that |A| = - 1, |B| = 3, then |3AB| =

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3 and 4 .Determinants and Matrices

easy

If $A $ and $ B$ are square matrices of order $3$ such that $|A| = - 1,$ $|B| = 3,$then $|3AB|$=

A

$-9$

B

$-81$

C

$-27$

D

$81$

(IIT-1988)

Solution

(b) $|A| = – 1,\,|B| = 3 \Rightarrow |AB| = – 3$

==> $|3AB| = {(3)^3}( – 3) = – 81$.

Standard 12

Mathematics

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