**Core Concept**
Beta-oxidation is the catabolic 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 the sequential removal of two-carbon units from the carboxyl end of the fatty acid chain.

**Why the Correct Answer is Right**
Beta-oxidation occurs in the mitochondrial matrix, where a series of enzyme-catalyzed reactions break down the fatty acid chain into acetyl-CoA units. The key enzymes involved in beta-oxidation, such as acyl-CoA dehydrogenase, enoyl-CoA hydratase, and 3-hydroxyacyl-CoA dehydrogenase, are all located in the mitochondrial matrix. The mitochondrial membrane plays a crucial role in maintaining the necessary environment for beta-oxidation to occur.

**Why Each Wrong Option is Incorrect**
**Option A:** Beta-oxidation does not occur in the cytosol, as the necessary enzymes and membrane-bound structures are not present in this compartment.
**Option C:** Lysosomes are involved in the breakdown of cellular waste and foreign substances, but they are not the site of beta-oxidation.
**Option D:** The Golgi apparatus is a complex organelle involved in protein modification and secretion, but it is not involved in the breakdown of fatty acids.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that beta-oxidation is a critical step in the breakdown of fatty acids, and defects in this process can lead to various metabolic disorders, such as medium-chain acyl-CoA dehydrogenase (MCAD) deficiency.

**✓ Correct Answer: B. Mitochondria**