Question

What is the determinant of an identity matrix?

Answer 1

The determinant of an identity matrix is always 1.

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.