$\DeclareMathOperator\soc{soc}$Let $\mathcal{A}$ be a unital semisimple Banach algebra.  The socle of $\mathcal{A}$, $\soc(\mathcal{A})$ is defined as the sum of the minimal right ideals (which equals to the sum of the minimal left ideals) or $\{0\}$ if there are none minimal right ideals. 

Let $\mathcal{B} = M_{2}(\mathcal{A}):=\{\left(
                                           \begin{array}{cc}
                                             a & c \\
                                             d & b \\
                                           \end{array}
                                         \right)
 : a,b,c,d \in \mathcal{A}$ \}. Then $\mathcal{B}$ be a unital semisimple Banach algebra. 
 What is the socle of $\mathcal{B}$? Is it true that $\soc(\mathcal{B}) =\soc(\mathcal{A}) \oplus  \soc(\mathcal{A})$?