Question

If A is a $3\times 3$ matrix such that $|5.adjA|=5,$ then $|A|$ is equal to

• A. $\pm \frac{1}{25}$
• B. $\pm 5$
• C. $\pm \frac{1}{5}$
• D. $\pm 1$

Answer 1

The correct option is C $\pm \frac{1}{5}$

Given,

$|5adjA|=5$

$\Rightarrow 125|adjA|=5$ ($|kA|=k^n|A|$ where $n$ is the order of matrix A.)

$\Rightarrow 125|A{|}^2=5$ ($|adjA|=|A{|}^{n-1}$, where n is order of matrix)

$\Rightarrow |A{|}^2=\frac{1}{25}$

$\Rightarrow |A|=\pm \frac{1}{5}$