Question

The Eigen values of a unit matrix of order 2 is
A) -1 and 1
B) 1 and -1
C) 0 and 1
D) 1 and 1 ​

Answer 1

Step-by-step explanation:

A) is correct option..

Answer 2

D) 1 and 1 ​are the Eigen values of a unit matrix of order 2

Step-by-step explanation:

Given: Unit matrix of order 2

To Find: the Eigen values of the given unit matrix

Solution:

• Finding the Eigen values of a unit matrix of order 2

We have given the unit matrix of order 2

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

Let the Eigen value be $\lambda$ such that it should satify the following condition;

$\Rightarrow | A - \lambda I | = 0$

$\Rightarrow \Big| \left[\begin{array}{cc}1&0\\0&1\end{array}\right] - \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] \Big| = 0$

$\Rightarrow \begin{vmatrix}1- \lambda&0\\0&1- \lambda \end{vmatrix} = 0$

$\Rightarrow (1- \lambda)^2 - 0 = 0$

$\Rightarrow (1- \lambda)^2 = 0$

$\Rightarrow \lambda = 1,1$

Hence, 1 and 1 ​are the Eigen values of a unit matrix of order 2