Question

If A and B are invertible matrices of same order such that |(AB)-1 | =8 .if |A|=2 then| B | is
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Answer 1

$\textbf{Given:}$

$\text{A and B are invertible matrices of same order and |(AB)^{-1}|=8 , |A|=8 }$

$\textbf{To find:}\;|B|$

$\textbf{Solution:}$

$\textbf{We know that,}$

$\textbf{If A and B are two non singular matrices of same order, then}$

$\bf(i)|A^{-1}|=\dfrac{1}{|A|}$

$\bf(ii)|AB|=|A|\,|B|$

$\text{Consider,}$

$|(AB)^{-1}|=8$

$\implies\dfrac{1}{|AB|}=8$

$\implies|AB|=\dfrac{1}{8}$

$\implies|A|\,|B|=\dfrac{1}{8}$

$\implies(2)|B|=\dfrac{1}{8}$

$\implies\bf|B|=\dfrac{1}{16}$

$\therefore\textbf{The value of \bf|B| is \bf\dfrac{1}{16} }$

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Answer 2

Step-by-step explanation:

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