Move constructor C++11

I am looking at some code that I have inherited and it has a matrix class which implements 2D matrices in C++ and has move constructors and assignment operator.

The way it is implemented is as follows:

template<typename T, int rows, int cols>
class matrix_data {
    ...
    std::unique_ptr<T[]> data_;
    // Some definitions
    typedef matrix_data<T, rows, cols> this_type

    matrix_data(this_type && other)
    {
        std::swap(data_, other.data_);
    }
};

Now, I am not sure why the data pointers are being swapped here. I thought it should be something like

data_ = std::move(other.data_);

I am guessing with the swap it is still ok because the other instance should be in an invalid state anyway after the move.

My question is whether I can replace the statement with data_ = std::move(other.data_); Is there some unique_ptr deletion stuff that is the reason for doing the swap instead of the move i.e. if I do the move would the original data be deleted correctly?