If $A$ and $B$ are square matrices of the same order $3$, such that $|A| = 2$ and $AB = 2I$, write the value of $|B|$.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 4 ##
$AB = 2I$
$\Rightarrow |AB| = |2I|$
$\Rightarrow |A| \cdot |B| = 2^3|I|$
$\Rightarrow 2 \times |B| = 8$
$\Rightarrow |B| = 4$