Matrices & Determinants
Adjoint determinant formula
Grade Class 12
Question:
If $M$ is a square matrix of order 3 such that $|M|=2$, then $\left|\text{adj}\!\left(\dfrac{M}{2}\right)\right|$ equals
$\dfrac{1}{2}$
$\dfrac{1}{4}$
$\dfrac{1}{8}$
$\dfrac{1}{16}$
Step-by-Step Solution
Key Concept: $|\text{adj}(A)|=|A|^{n-1}$ for $n\times n$ matrix. $|M/2|=|M|/2^3=2/8=1/4$. $|\text{adj}(M/2)|=(1/4)^{3-1}=1/16$.
$|\text{adj}(M/2)|=(1/4)^2=1/16$.
Correct Answer: 4