Question

Given eigenvalues 1,-1,0 then find determinant of i+a^100

Answer 1

Answer:

eigen values of matrix a = 1, -1, 0

So, | a -AI |=0, where A=1

Also, | a -B I  |=0, Where B= -1------(1)

And , | a - C I  |=0, where , C=0

Consider equation (1)

When , B= -1,

$| a +I|=0 \\\\{\text{Taking 100 th power on both sides}}\\\\ |a +I|^{100}=(0)^{100}\\\\ |a + I |^{100}=0$