If $A$ is a square matrix satisfying $A'A = I$, write the value of $|A|$.

$\pm 1$

The correct answer is Option (3) → $\pm 1$ ##

Let the value of $|A| = x$

Since, $|A| = |A'|$ and $|I| = 1$

Given, $AA' = I$

$∴|AA'| = |I|$

$\Rightarrow |A||A'| = |I| \quad [ ∵|AA'| = |A||A'| ]$

$\Rightarrow x \cdot x = 1$

$\Rightarrow (x^2 - 1) = 0$

$\Rightarrow (x - 1)(x + 1) = 0 \Rightarrow x = \pm 1$

$∴|A| = \pm 1$