Question

$$\text {What is the degree of the determinant }\left|\begin{array}{ll}a & b \\c & d\end{array}\right|$$$$\text{ ?}$$

Answer 1

Correct option is D. $$2$$

$$\textbf{Step 1: Expand the determinant and then check the degree of polynomial.}$$

$$\left|\begin{array}{ll}a & b \\c & d\end{array}\right|=ad-bc$$

$$\text{degree of }ad =1+1=2$$

$$\text{degree of }bc=1+1=2$$

$$\text{Hence, highest power is 2}$$

$$\Rightarrow \text{degree of the given determinant is 2}$$

$$\textbf{Hence, Option D is correct.}$$