Matrix dimension by itself have little todo with PCA validity. What will change is the interpretation of your data and it's all dependent on how you want to use the result.
PCA is very powerful to use to find anomalys or outliers in your data. Maybe you have performed an experiment on two different days, used different machines in the experiment etc. If the purpose is to get an overview of data PCA is one of the most efficient way to do that regardless of any n/m ratios.
If your main interest is to investigate clusters or relations between samples, then #variables are not very important. (But other type of statistics on the result might be important if #samples are low).
If you look at individual variables, then they will be less reliable if you have few samples. However, this is a problem you will have with any other method as well. If you find patterns among variables that make sense then you should certainly not disregard your findings because you have a low n/m ratio. However, few observations are almost allways problematic and should lead to caution in interpretation and the more samples you have the less important is the #sample/#variable relation.