Question

What is the determinant of an identity matrix?

Answer 1

Nonexistent
Consider M2(R) for a,b,c,d in R.
det (M2 (R))=ad-bc=0 for identity yet limx->0 (1/x)
DNE therefore it is Undefined.

Answer 2

Answer:

The determinant of an identity matrix is always 1.

Step-by-step explanation:

Given : An identity matrix.

We have to find the determinant of an identity matrix.

Consider an identity matrix,

Identity matrix is a matrix having entry one in its diagonal and  rest all entries are zero.

Let us consider a 2 × 2 identity matrix,

$I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

We know determinant of a  2 × 2 matrix

$I=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]$

is given by

D = ad - bc

Thus, here a = 1 , b = 0 , c= 0 d= 1

Thus, D = 1 - 0 = 1

Thus, The determinant of an identity matrix is always 1.