True or False Solutions required Thanks Suppose A elementof

True or False?

Solutions required.

Thanks.

Suppose A elementof R^n times n satisfies the property A^2 = A then sigma (A) = {0, 1}, True False

Solution

Since we have A^2 = A then we can see that A is an  idempotent matrix. And we know that the eigen value of an  idempotent matrix is either 1 or zero.

And also a Pauli\'s matrix can be written as a set of 2*2 matrix which has 1 and 0 as elements. Hence we can say that (A)= {0,1}.

Hence, given statement is true.