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Matrics — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsMatrics2 Marks
MCQ
If $A$ is a singular matrix, then $\operatorname{adj} A$ is
  • ✓
    singular
  • B
    non-singular
  • C
    symmetric
  • D
    not defined
✓

Answer

Correct option: A.
singular
(A) Given, A is a singular matrix.
$\therefore \quad| A |=0$
Using Shortcut 4(viii),
$|\operatorname{adj} A |=| A |^{ n -1}$
$\Rightarrow|\operatorname{adj} A|=0$
$\Rightarrow \operatorname{adj} A$ is also singular.

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