I am aware that there exists another property of determinants NOT mentioned in the book,
namely: the linearity of a single row(column) for addtition:
| A + A' B + B' | = | A B | + | A' B' |
| C D | | C D | | C D |
Can we use this property in the exam/quiz without the proof?
Good job. It's true for a single row(column) addition.
Someone can prove this by using the cofactor expansion along that row(column).
You may use this, but you have to write some additional description.