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Injecting a vaccine with an inactive antigen and observing the antibody response is the appropriate method to confirm the formation of memory B cells in mice after multiple infections.

When a vaccine contains inactive antigens, it simulates an infection without causing disease, prompting the immune system to respond. Memory B cells are a critical component of the adaptive immune response; they are formed following initial exposure to an antigen and are responsible for the quicker and stronger antibody production upon subsequent exposures to the same antigen. By administering the inactive antigen and monitoring the antibody response, scientists can evaluate whether memory B cells have been successfully generated. A strong antibody response would indicate that memory B cells are present and that the immune system is effectively recalling the immune memory from previous infections.

The other methods listed do not provide direct evidence regarding the formation of memory B cells. Injecting an active antigen could lead to a response but does not specifically confirm the existence of memory cells resulting from previous infections. Measuring body temperature during vaccination is not relevant to memory B cell formation, as it doesn't assess the immune response directly. Observing the diet of the mice post-infection does not relate to immune memory or the presence of memory B cells at all. Thus, monitoring the antibody response to an inactive antigen gives the most