Let
$$A=\left[\begin{array}{ll}a_{11} & a_{12} \\a_{21} & a_{22}\end{array}\right], B=\left[\begin{array}{ll}
b_{11} & b_{12} \\b_{21} & b_{22}\end{array}\right], \text { and } C=\left[\begin{array}{ll}c_{11} & c_{12} \\c_{21} & c_{22}\end{array}\right]$$
where all the elements are real mumbers. Use these matrices to show that each statement is true for $2 \times 2$ matrices.
$c(A+B)=c A+c B,$ for any real number $c$.