1. The problem asks to evaluate the limit of a matrix as $x$ approaches $a$, specifically $$\lim_{x \to a} \begin{bmatrix} a & b \\ c & d \end{bmatrix}.$$\n\n2. Since the matrix entries $a$, $b$, $c$, and $d$ are constants (do not depend on $x$), the limit of the matrix as $x$ approaches $a$ is simply the matrix itself.\n\n3. The limit of a matrix is found by taking the limit of each individual element. Here, each element is constant, so:\n$$\lim_{x \to a} a = a,$$\n$$\lim_{x \to a} b = b,$$\n$$\lim_{x \to a} c = c,$$\n$$\lim_{x \to a} d = d.$$\n\n4. Therefore, the limit matrix is:\n$$\begin{bmatrix} a & b \\ c & d \end{bmatrix}.$$\n\n5. In summary, when the matrix elements are constants, the limit as $x$ approaches any value is the matrix itself.