What is the value of the determinant of an identity matrix of order $3$?

Solution

1. The identity matrix of order $3$ is defined as $I_3=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right)$.
2. The determinant of a diagonal matrix is equal to the product of the entries on its main diagonal.
3. Calculating the product, we get $$\begin{array}{rl}\det (I_3)& =1\times 1\times 1\\ & =1\end{array}$$.
4. Hence the answer is (B).