Question

If A and B are square matrices of order 3 such that|A| =1 ,|B|=3 , write the value of det |(-2A)B'|

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Answer 1

$\textbf{Given:}$

$\text{A and B are square matrices of order 3 and |A|=1,\;|B|=3 }$

$\textbf{To find:}$

$\text{The value of |(-2A)B'| }$

$\textbf{Solution:}$

$\text{We know that,}$

$\textbf{A and B are two matrices of same order n.}$

$\textbf{Then,}$

$\bf(i)\;|AB|=|A|\,|B|$

$\bf(ii)\;|kA|=k^n\,|A|$

$\bf(iii)|A'|=|A|$

$\text{Consider,}$

$|(-2A)B'|$

$=|-2A|\;|B'|$

$=(-2)^3|A|\;|B|$

$=(-8)|A|\;|B|$

$=(-8)(1)(3)$

$=-24$

$\textbf{Answer:}$

$\textbf{The value of \bf|(-2A)B'| is -24}$

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