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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
If $\text{A} = \begin{bmatrix}1&\text{amp; } \log_{\text{b}}\text{a}\\ \log_\text{a}\text{b}&\text{amp; } 1\end{bmatrix}$then $ |\text{A}|$ is equal to:
  • ✓
    $0$
  • B
    $\log_\text{a}\text{b}$
  • C
    $-1$
  • D
    $\log_\text{b}\text{a}$
✓

Answer

Correct option: A.
$0$
On solving the given matrix,
$|\text{A}|=1-\log_\text{a}\text{b}.\log_\text{b} \text{a}=1-1=0$

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