Given - $$K_{3\times3} = \begin{bmatrix} 1&1&1 \\ 3&2&1 \\ 1&2&1 \end{bmatrix}$$ $$|K| = 2$$ Find - $$|2K^3-2K^4|$$
I tried this:
Since $|A+B|=|A|+|B|$ ( $\Leftarrow$ This is the main mistake ) - $$|2K^3-2K^4|=|2K^3+(-2K^4)|=|2K^3|+|(-2K^4)|$$
Now using $|\alpha A_{n\times n}|=\alpha ^n|A|$ - $$=2^3|K^3|+(-2^4)(K^4)|=8*8+(-16)*16=-192$$