practice book gate

Question

the eigen values of the matrix are

 

(a) (a+1), 0

(b) a, 0

(c)  (a-1), 0

(d) 0, 0

Answer 1

Let x and y be the eigen values of the matrix 

So according to properties of the matrix

Sum of eigen value =  Trace of the matrix i.e sum of diagonal element 

Product of eigen value = Determinant of matrix

∴ x+y = a+1   and   xy= 0

Solving y=0 then  x= a+1

So option A is correct