Final answer:
a) Matrix multiplication is not applicable in the context of the energy states of an oscillator in quantum mechanics. The nth energy state is not independent of matrix multiplication, but the two are unrelated concepts.
Step-by-step explanation:
Matrix multiplication is not applicable in this context because the question is asking about the energy states of an oscillator in quantum mechanics, which is a different mathematical framework than matrix multiplication. The energy states of an oscillator in quantum mechanics are determined by the principal quantum number, not matrix multiplication. The specific matrix product is not provided in this context because it is not applicable. The nth energy state is not independent of matrix multiplication because matrix multiplication is not applicable to this context. Matrix multiplication is not inversely proportional to the energy state because they are unrelated concepts in quantum mechanics.