The correct answer is B) False.
RNA polymerase I is primarily responsible for synthesizing ribosomal RNA (rRNA) in eukaryotic cells, not messenger RNA (mRNA). While transcription is a critical process in gene expression, different types of RNA polymerases are specialized for different types of RNA. In eukaryotes, RNA polymerase II is the enzyme that transcribes mRNA from DNA. This differentiation is important because each type of RNA plays a unique role in the cell. Therefore, it is incorrect to assign the function of mRNA production to RNA polymerase I.