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Matrices (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)1 Mark
MCQ
If $A$ is a non-singular matrix, then $\operatorname{det}\left( A ^{-1}\right)=$
  • A
    1
  • B
    $0$
  • C
    $\operatorname{det}( A )$
  • ✓
    $1 / \operatorname{det}(A)$
✓

Answer

Correct option: D.
$1 / \operatorname{det}(A)$
(d) $1 / \operatorname{det}(A)$
Hint:
$
\begin{aligned}
& A A^{-1}=1 \\
& \therefore|A| \cdot\left|A^{-1}\right|=1 \\
& \therefore\left|A^{-1}\right|=\frac{1}{|A|}
\end{aligned}
$

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