Question

If A is a non singular matrix of order 3,then|adj.A|=​

Answer 1

$\textbf{Given:}$

$\text{A is a non-singular matrix of order 3}$

$\textbf{To find:}$

$|adjA|$

$\textbf{Solution:}$

$\text{We know that,}$

$\text{If A is a square matrix order n, then}$

$\bf\,A(adjA)=(adjA)A=|A|\,I_n$

$\implies\,(adjA)A=|A|\;I_n$

$\text{Taking determinant}$

$|(adjA)A|=||A|\;I_n|$

$|adjA|\;|A|=|A|^n|I_n|$

$|adjA|\;|A|=|A|^n(1)$

$|adjA|\;|A|=|A|^n$

$|adjA|=\dfrac{|A|^n}{|A|}$

$\implies|adjA|=|A|^{n-1}$

$\textbf{Answer:}$

$\boxed{\bf|adjA|=|A|^{n-1}}$

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