Question

If I₃ denotes identity matrix of order 3 × 3, write the value of its determinant.

Answer 1

In an identity matrix, all the diagonal elements are 1 and rest of the elements are 0.
Here,
\[I_3 = \begin{vmatrix} 1 & 0 & 0\\0 & 1 & 0\\0 & 0 & 1 \end{vmatrix}\] 
\[ = 1 \times \begin{vmatrix} 1 & 0\\0 & 1 \end{vmatrix} \left[\text{ Expanding along }C_1 \right]\] 
\[ = 1\] 
\[ \Rightarrow I_3 = 1\]