if tr(A)= 2+i then tr[(2-i)A] = 
(1) 5
(2) 4
(3) 3
(4) -4 

Dear student, 

We can use the properties of trace to solve this question. 

We know that trace is a linear mapping. That is:

tr (A + B) = tr(A) + tr(B) and 
tr(cA) = ctr(A) 
for all square matrices A and B, and all scalars c.

So we can now write:

tr [(2 - i)A] = tr [2A - iA] = tr [2A] - tr[iA] = 2*tr[A] - i*tr[A] = 2(2 + i) - i*(2 + i) = 4 + 2i - 2i - i² = 4 + 1 = 5

Hence, correct answer for this will be option 1.

Regards