Question

If A is any square matrix of order 3 × 3 such that |A| = 3, then the value of
|adjA| is ?
(a) 3 (b) 1/3 (c) 9 (d) 27

Answer 1

$\textbf{Given:}$

$\text{A is a 3{\times}3 square matrix and }\;|A|=3$

$\textbf{To find:}$

$\text{The value of }\;|adjA|$

$\textbf{We know that,}$

$\textbf{If A is a square matrix of order n, then}\;\bf|adjA|=|A|^{n-1}$

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

$\implies|adjA|=|A|^{3-1}$

$\implies|adjA|=|A|^{2}$

$\implies|adjA|=(3)^{2}$

$\implies\boxed{\bf|adjA|=9}$

$\therefore\textbf{The value of |adjA| is 9}$

$\implies\textbf{option (c) is correct}$

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