Step-by-Step Solution
Key Concept: The binomial theorem can be applied to the matrix expression $(I+A)^n$ because the identity matrix commutes with any matrix $A$, allowing the expansion to simplify to $I + nA$ if $A^2$ and all higher powers are the zero matrix.
$(I + A)^{100} = ^{100}C_0 I^{100} + ^{100}C_1 I^{99}A + ^{100}C_2 I^{98}A^2 + \dots + ^{100}C_{100}A^{100} = I + 100A + O + O + \dots + O = I + 100A$
Correct Answer: D