Step-by-step explanation:
Let's consider C is a matrix given by
[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex]
them determinant of matrix C can be written as
[tex]\begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}\ =\ 4.....(1)[/tex]
Now,
[tex]det (C+C)\ =\ \begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}\ +\ \begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}[/tex]
[tex]=\ \begin{vmatrix}2a & 2b & 2c\\ 2d & 2e & 2f\\ 2g & 2h & 2i \end{vmatrix}[/tex]
[tex]=\ 2\times 2\times 2\times \begin{vmatrix}a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}[/tex]
[tex]=\ 8\times 4\ \ \ \ \ \ \ \ from\ eq.(1)[/tex]
= 32
Hence, det (C+C) = 32
