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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
For an invertible matrix $A$ if $A(\operatorname{adj} A)$ $=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]$, then $|A|$ is
  • A
    100
  • B
    -100
  • ✓
    10
  • D
    -10
✓

Answer

Correct option: C.
10
(c) : We have, $A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]=10\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]=10 I$
We know that $A(\operatorname{adj} A)=|A| I \Rightarrow|A|=10$

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