If \( \begin{vmatrix}x & 2\\18 & x\end{vmatrix}=\begin{vmatrix}6 & 2\\18 & 6\end{vmatrix} \) , then \( x \) equals:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ±6
Expanding both determinants:
\( \displaystyle x^2-36=36-36=0 \)
\( \displaystyle x^2=36\ \Rightarrow\ x=\pm 6 \)
Why the other options are incorrect
Option (1) 0 — Incorrect. At x = 0 the left side is −36, not 0.
Option (2) 6 — Incorrect. x = 6 is a solution, but it is not the only one; −6 also gives \( x^2=36 \).
Option (3) −6 — Incorrect. x = −6 is a solution, but 6 is also a solution.
NCERT (2026-27 edition):
Determinant
