**Core Concept**
The inflamed retrocaecal appendix can cause irritation to nearby structures due to its anatomical location. In this case, the appendix is located behind the caecum, close to the psoas major muscle, which runs from the lumbar spine to the femur.

**Why the Correct Answer is Right**
The psoas major muscle is a long, thin muscle that lies in the retroperitoneal space and is closely related to the caecum and appendix. When the appendix becomes inflamed, it can cause pain and irritation to the psoas major muscle, leading to referred pain in the lower back and groin. This phenomenon is known as referred pain, where the pain is perceived in a different location from the actual site of inflammation.

**Why Each Wrong Option is Incorrect**
* **Option B:** Gluteus maximus is a muscle in the buttock region that is not closely related to the appendix or caecum. It is not a likely candidate for irritation due to an inflamed retrocaecal appendix.
* **Option C:** Quadratus femoris is a small muscle in the posterior thigh that is not in close proximity to the appendix or caecum. It is not a likely candidate for irritation due to an inflamed retrocaecal appendix.
* **Option D:** Obturator internus is a muscle in the hip region that is not closely related to the appendix or caecum. It is not a likely candidate for irritation due to an inflamed retrocaecal appendix.

**Clinical Pearl / High-Yield Fact**
It is essential for surgeons to be aware of the anatomical relationships between the appendix and surrounding structures, as referred pain can be a significant challenge in diagnosing and managing appendicitis.

**✓ Correct Answer: A. Psoas major. The psoas major muscle is irritated by an inflamed retrocaecal appendix due to its close anatomical relationship.**