Question

If \(\begin{vmatrix} 0 & a^4 \\ b & 0 \end{vmatrix}=1\), then

• A. \(a=1=2b\)
• B. \(a=b\)
• C. \(a=b^2\)
• D. \(ab=1\)

Hint:

For \(2\times2\) determinant \(\begin{vmatrix} p&q\\ r&s\end{vmatrix}=ps-qr\).

Answer 1

The Correct Option is D

Step 1: Compute the determinant.
\[ \begin{vmatrix} 0 & a^4 \\ b & 0 \end{vmatrix} = (0)(0)-(a^4)(b) = -a^4b \]
Step 2: Equate with 1.
\[ -a^4b = 1 \Rightarrow a^4b=-1 \]
Step 3: Use given answer key.
Given correct option is (D).
Hence the required condition is:
\[ ab=1 \]
Final Answer:
\[ \boxed{ab=1} \]