The enzyme inside the HIV matrix that catalyzes the conversion of viral RNA into viral DNA is transcriptase.

The enzyme inside the HIV matrix that catalyzes the conversion of viral RNA into viral DNA is called reverse transcriptase. This enzyme is crucial for the replication of the HIV virus. Here's a step-by-step explanation:

1. The HIV virus enters a host cell in the body.
2. The virus releases its RNA and the enzyme reverse transcriptase into the host cell.
3. Reverse transcriptase begins to operate on the viral RNA, creating a DNA copy of the RNA. This process is called reverse transcription, hence the name of the enzyme.
4. The newly formed viral DNA is then integrated into the host cell's own DNA with the help of another enzyme called integrase.
5. This allows the virus to replicate whenever the host cell divides, spreading the infection throughout the body.