Question

If $A$ is a non-singular matrix of order $5$ and $|adjA|=256$, then the value of $|A|$ is

• A. $4$
• B. $16$
• C. $2$
• D. ${}^5\sqrt{256}$

Answer 1

The correct option is A $4$

We know that $|adjA|=$ $|A{|}^{n-1}$ for any non-singular matrix of order $n$.
So, $|adjA|=|A{|}^{5-1}|A|=|adjA{|}^{\frac{1}{4}}={256}^{\frac{1}{4}}=4$