In the context of a government agency using the Business Rules Engine (BRE) to calculate and determine Households Area Median Income (AMI) prioritization using a matrix, the BRE designer should use two decision matrices (Option C). One matrix is necessary to calculate the AMI and to evaluate it against the federal income limits, which involves determining the percentage of AMI relative to these limits. The second matrix is then used to categorize these percentages into different prioritization pools. This allows for a clear separation of logic in handling the data: one matrix for the determination of AMI percentages and another for the allocation into prioritization pools based on these percentages.

Option A and D, which suggest using only one matrix, would not provide the necessary separation of calculations and evaluations for clarity and maintenance. Option B suggests using three matrices, which overcomplicates the process without clear necessity for three separate matrices when two are sufficient for the tasks at hand.