If X is a square matrix of order 3 3 and is a scalar, then adj ( … - Vidyadip

MCQ

If X is a square matrix of order $3 \times 3$ and $\lambda$ is a scalar, then adj $(\lambda X)$ is equal to

A
$\lambda \operatorname{adj} X$
B
$\lambda^3 \operatorname{adj} X$
✓
$\lambda^2 \operatorname{adj} X$
D
$\lambda^4 \operatorname{adj} X$

✓

Answer

Correct option: C.

$\lambda^2 \operatorname{adj} X$

(C) $\operatorname{adj}(\lambda X )=\lambda^{3-1}(\operatorname{adj} X )$
…[Using Shortcut 4(vi)]
$=\lambda^2 \operatorname{adj} X$

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