**Core Concept**
Beta oxidation of fatty acids is a process by which fatty acids are broken down into acetyl-CoA units, which can then be fed into the citric acid cycle for energy production. This process involves a series of enzyme-catalyzed reactions that take place in the mitochondria.

**Why the Correct Answer is Right**
Beta oxidation occurs in the mitochondrial matrix, where the enzymes involved in this process are located. The process begins with the activation of fatty acids to their CoA derivatives, followed by the removal of two-carbon units (as acetyl-CoA) through a series of reactions catalyzed by acyl-CoA dehydrogenase, enoyl-CoA hydratase, 3-hydroxyacyl-CoA dehydrogenase, and 3-ketoacyl-CoA thiolase. These reactions result in the progressive shortening of the fatty acid chain until it is fully oxidized to acetyl-CoA units.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because beta oxidation does not occur in the cytoplasm. While some steps in fatty acid metabolism do take place in the cytoplasm, the actual beta oxidation process occurs in the mitochondria.
**Option B:** This option is incorrect because peroxisomes are involved in the beta oxidation of very-long-chain fatty acids, but not in the general beta oxidation of fatty acids.
**Option C:** This option is incorrect because the endoplasmic reticulum is involved in the synthesis of fatty acids, not their breakdown through beta oxidation.

**Clinical Pearl / High-Yield Fact**
It's worth noting that defects in beta oxidation can lead to a range of clinical disorders, including carnitine palmitoyltransferase II (CPT II) deficiency, which can cause muscle weakness, myoglobinuria, and other symptoms.

**Correct Answer: C. Mitochondrial matrix.**