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 × 3$ and $\lambda $ is a scalar, then adj ($\lambda X)$ is equal to

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

✓

Answer

Correct option: C.

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

c
(c) By fundamental property, $adj(\lambda X) = {\lambda ^{n - 1}}(adj\,X)$.

Here $n = 3$

$\therefore$ $adj(\lambda X) = {\lambda ^{3 - 1}}(adj\,X)$

$adj(\lambda X) = {\lambda ^2}(adj\,X)$.

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