1.

Let A denote the matrix `({:(0,i),(i,0):})`, where ` i^(2) = -1` , and let `I` denote the identity matrix `({:(1,0),(0,1):})`. Then `I + A + A^(2) + "….." + A^(2010)` is -A. `({:(0,0),(0,0):})`B. `({:(0,i),(i,0):})`C. `({:(1,i),(i,1):})`D. `({:(-1,0),(0,-1):})`

Answer» Correct Answer - C
`A = [{:(0,i),(i,0):}] , A^(2) = [{:(-1,0),(0,-1):}], A^(3) = [{:(0,-i),(-i,0):}] , I = [{:(1,0),(0,1):}]`
` I + A + A^(2) + A^(3) = [{:(0,0),(0,0):}] , A^(4) = [{:(1,0),(0,1):}] = 1`
`I + A + A^(2) + A^(3) + "......"A^(2010)`
` (I + A + A^(2) + A^(3)) + A^(4)(I + A + A^(2) + A^(3))+"......"+A^(2008)(I+A+A^(2))`
`= ({:(1,i),(i,1):})`


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