Use single Convolution layer for the classification of two kinds of matrix?
A Convolution neural network is not justified here.
CNN is used for images because -

Flattening the data can create very high dimensional features


Exerpt from &quot;Hands-on Machine Learning&quot; book -
For example, a 100 × 100–pixel image has 10,000 pixels, and if the first layer has just 1,000 neurons (which already severely restricts the amount of information transmitted to the next layer), this means a total of 10 million connections.
2. Nearby pixels tell a lot about the feature. So by using convolution, Pooling, we are able to reduce the dimension without losing information. The best part is that learning(Identifying the features) is part of Backpropagation
3. Weight sharing reduces the parm count further

 In the case mentioned in the question -

Dimension is not so large i.e. 10x10 = 100
Data is sparse and binary. I doubt it can represent spatial features. CNN is not good for sparse dataset.
Only one kernel

I doubt real CNN is happening in the background. You are getting one Feature map and then it is flattened to work as a normal Neural network.
So, it would be better to use a normal neural network
Before that, you should try SVM once as it works well on the sparse dataset. Though data-count is a bit large but can try once.