if f:S-S is a function over set S, where S is a set of all square matrices and f(x)= x²-5x+6. find f(A) if A= 2 0 1

2 1 3

1 -1 0 its a 3*3 matrice

Dear Student,

f(A) = A² – 5A + 6I,
Find A², 5*A and 6I which will come out to be
A2 = [5 -1 2: 9 -2 5: 0 -1 -2]
5A = [10 0 5: 10 5 15: 5 -5 0]
6I = [6 0 0: 0 6 0: 0 0 6]
Now just put this values and apply the algebric operation as given

Thanks.