WBJEE · Maths · Determinants
The determinant \(\left|\begin{array}{ccc}a^{2}+10 & a b & a c \\ a b & b^{2}+10 & b c \\ a c & b c & c^{2}+10\end{array}\right|\) is
- A divisible by 10 but not by 100
- B divisible by 100
- C not divisible by 100
- D not divisible by 10
Answer & Solution
Correct Answer
(B) divisible by 100
Step-by-step Solution
Detailed explanation
=\frac{1}{a b c}\left|\begin{array}{ccc}a\left(a^{2}+10\right) & a^{2} b & a^{2} c \\ a b^{2} & b\left(b^{2}+10\right) & b^{2} c \\ a c^{2} & b c^{2} & c\left(c^{2}+10\right)\end{array}\right|=\frac{a b c}{a b c}\left|\begin{array}{ccc}a^{2}+10 & a^{2} & a^{2} \\ b^{2} &…
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