CUET Preparation Today
If $A$ is a square matrix of order 3 such that $A^2 = 2A$, then find the value of $|A|$. |
$0$ or $2$ $0$ or $8$ $2$ or $4$ $8$ only |
$0$ or $8$ |
The correct answer is Option (2) → $0$ or $8$ ## $A^2 = 2A$ $\Rightarrow |A^2| = |2A|$ $\Rightarrow |A||A| = 8|A|$ $(∵|AB| = |A||B| \text{ and } |2A| = 2^3|A|)$ $\Rightarrow |A|(|A| - 8) = 0$ $\Rightarrow |A| = 0 \text{ or } 8$ |
