Confusion matrix to check results
A confusion matrix is indeed a very useful way to analyze the results of your experiment. It provides the exact number (or percentage) of instances with true class X predicted as class Y for all the possible classes. As such it gives a detailed picture of what the system classifies correctly or not.
But a confusion matrix is a bit too detailed if one wants to summarize the performance of the classifier as just one single value. This is useful especially when one wants to compare two different classifiers, since there's no general way to compare two confusion matrices. That's why people often use evaluation measures: for binary classification, the most common ones are:

Accuracy, which is simply the number of correct predictions divided by the total number of instances.
F-score, which itself is the harmonic mean of precision and recall. Quite ironically, F-score gives a more accurate picture of performance than accuracy because it takes into account the different types of possible errors.