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What are the eigenvalues of the following $2\times 2$ matrix? $$\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$

1. -1 and 1
2. 1 and 6
3. 2 and 5
4. 4 and -1

Let the eigen values be a,b

Sum of Eigen Values = Trace(Diagonal Sum)

=> a+b = 2+5 = 7

Product of Eigen Values = Det(A)

=> a.b = 6

Solving these we  get 1 and 6.. So, Option(B) is Correct ..

selected
how did you derived this?
these are famous properties..
will this work as check for matrices of size grater than 2*2
always, for n*n matrices.
(2-x)(5-x)-4=0 x=1,6