Question

if A is the third order matrix and |adjA|=256 then what is the value of |A
|​

Answer 1

Answer:  |A|=16

Given:

$\sf\text{Order of matrix of A (n)=3 }\\\\left|\begin{array}{c}adjA\end{array}\right|=256$

To find:

$\sf\text{The value of }\left|\begin{array}{c}A\end{array}\right|$

Explanation:

$\sf\text{We know that,}$

$\fbox{\sf \left|\begin{array}{c}adjA\end{array}\right|=\left|\begin{array}{c}A\end{array}\right|^{n-1} }$

$\sf\text{According to the question,}$

$\sf n=3\ and \left|\begin{array}{c}adjA\end{array}\right|=256.\\\\\sf\text{Substituting the values in the formula, we get:}$

$\Rightarrow\sf 256=\left|\begin{array}{c}A\end{array}\right|^{3-1} }$

$\Rightarrow\sf 256=\left|\begin{array}{c}A\end{array}\right|^{2} }$

$\Rightarrow\sf \sqrt{256} =\left|\begin{array}{c}A\end{array}\right| }$

$\Rightarrow\sf \left|\begin{array}{c}A\end{array}\right|=16 }$

$\sf\textbf{Hence the value of \left|\begin{array}{c}A\end{array}\right| \sf is\:\underline{16} }$