If $A$ is a square matrix of order 3 such that $A^2 = 2A$, then find the value of $|A|$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $0$ or $8$ ##
$A^2 = 2A$
$\Rightarrow |A^2| = |2A|$
$\Rightarrow |A||A| = 8|A|$
$(∵|AB| = |A||B| \text{ and } |2A| = 2^3|A|)$
$\Rightarrow |A|(|A| - 8) = 0$
$\Rightarrow |A| = 0 \text{ or } 8$