What is the determinant of an identity matrix?

Question

asked Jul 2, 2017 131k views

1 Answer

Al Joslin · Answer 1 · 2017-07-06T15:00:34+0000

Answer:

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.