Consider the following network:
The numbers represent certain basic operations on a matrix as follows:
0: simply XOR the input matrices
1: simply OR the input matrices
2: XOR the input then invert the result
3: OR the input then invert the result
4: XOR the input then transpose the resulting matrix
5 OR the input then transpose the resulting matrix
6 XOR the input then shift the result so the left half and the right half of the matrix are exchanged
7 OR "
8 XOR the input then flip the result vertically
9 OR "
With these elementary operations and this network configuration:
So this network works pretty well for detecting whether the input matrix is one of the two in the picture above, and doesn't return True very often for any input matrix other than those two.
Now this was a simple problem that you probably wouldn't solve this way but would instead solve directly checking for the particular two inputs, but I see it as a proof of concept and I will be trying to use this method to solve over more complicated input, like non-binary or more complex patterns to return True on.