Is this classifier random? I trained a classifier and got the following stats on some test data:
    Correctly Classified Instances        1059               95.1482 %
    Incorrectly Classified Instances        54                4.8518 %
    Kappa statistic                          0     
    Mean absolute error                      0.0485
    Root mean squared error                  0.2203
    Total Number of Instances             1113     

    === Detailed Accuracy By Class ===

           TP Rate   FP Rate   Precision   Recall  F-Measure   ROC Area  Class
             1         1          0.951     1         0.975      0.5      0
             0         0          0         0         0          0.5      1
Weight Avg.  0.951     0.951      0.905     0.951     0.928      0.5

Since my kappa and ROC Area (for both classes) are $0$ and $0.5$, respectively, have I learned a random classifier?
EDIT
=== Confusion Matrix ===

    a    b   <-- classified as
 1059    0 |    a = 0
   54    0 |    b = 1

 A: You haven't build a random classifier, instead you have built one that always gives the same answer: "0". The reason why it performs good as measured in accuracy, is that accuracy just looks at whether the classification is right or not and is not class-specific. Basically, you have an accuracy of 95% because that is exactly the prevalence of class 0. 
To put it in everyday terms, consider telling everyone you meet that they do not have brain cancer. You will be right almost every time (Accuracy >> 99%). But that's trivial, since it's so rare. Now, do the same to persons who come to the hospital with a set of symptoms that fit brain cancer and you will suddenly be much more inaccurate if you tell everyone that they are fine.
The fact that it depends heavily on prevalence is the reason that other measures (like AUC or balanced accuracy) are preferred instead of accuracy.
A: You can build the confusion matrix from TP Rate, FP Rate, Precision, Recall and a few other pieces of information you gave. You'll see that your classifier's predictions are always class 0. It's different from a random classifier, but not that much more useful.
A: As mentioned by others, you are learning a classifier that always predicts the most frequent class. This sometimes happens in unbalanced classification problems.
One solution is to use instance weighting. Many classifiers allow you to associate each instance with a numerical weight representing how important it is to classify that instance correctly. To balance your problem, simply associate each instance with a weight that is inversely proportional to the frequency of its class. Some classifiers can do this balance automatically by doing this calculation on their own - check for appropriate flags.
For example, if you have 90 a instances and 10 b instances, give the a instances a weight of $1/10$ and give the b instances a weight of $9/10$, so that the sum of the weights of the as is equal to the sum of the weights of bs.
