Find the Jacobson radical of matrix ring $R=\mathbf{M}_2(K\otimes_kK)$ where $k =\mathbb{F}_2[x]$ and $K = \mathbb{F}_2[x^{1/2}]$
I tried to find the radical of this matrix ring. I have also found the solutions of the radical of those upper triangular matrix ring. But I don't think this question is the same kind of that. Please help me! Thanks in advance!!