Step 1: Evaluating the Assertion (A)
M13 is a filamentous bacteriophage containing a single-stranded circular DNA genome ($+$ strand). Upon entry into the E. coli host cell, the single-stranded DNA is converted into a double-stranded replicative form (RF) DNA by host enzymes. This dsRF DNA replicates using the rolling circle replication mechanism to amplify the viral genome. Thus, Assertion (A) is true.
Step 2: Evaluating the Reason (R)
During rolling circle replication, the host cell synthesizes the complementary strand, forming the dsRF. This replicative form replicates continuously to yield approximately $100 - 200$ copies of dsRF per host cell. Thus, Reason (R) is true.
Step 3: Logical Connection
The rolling circle replication mechanism is the specific biological process that allows the virus to produce its double-stranded replicative forms and amplify its genome copies. Hence, R is the correct biological explanation for how M13 replicates its circular DNA inside host cells.
Step 4: Conclusion
Both are true, and R is the correct explanation of A, matching option (A).
Final Answer: (A)