Complete the pattern

Question

I have been creating puzzles to promote our school's Facebook page, but in a week no-one could yet answer this one:

Complete the pattern:

Answer 1

It is:

C

because:

Let white=0, grey=1, black=2. Adding the first two squares from either rows or columns and subtract 3 if the answer is greater than 2 gives the third square in the row/column.

Answer 2

Answer is:

C

Because:

Black + black = gray.
Gray + gray = black.
Color + white = color.

Answer 3

The answer is:

C.

Due to:

Assign black, grey, and white the values, and 0 respectively (Black would be 2, grey 1, and white 0). Now the top-left square would look like this: $$\begin{bmatrix}2 & 1 & 0\\1 & 2 & 1 \\0 & 1 & 2 \end{bmatrix}$$ And the middle-left like this: $$\begin{bmatrix}0 & 0 & 0\\1 & 1 & 1 \\2 & 2 & 2 \end{bmatrix}$$ Adding them together would result in a square looking like this: $$\begin{bmatrix}2 & 1 & 0\\2 & 3 & 2 \\2 & 3 & 4 \end{bmatrix}$$ Which has values greater than 2, so we use a modulo function (which gives the remainder of a division) to subtract three from all values greater than 2, gives a box with the following values: $$\begin{bmatrix}2 & 1 & 0\\2 & 0 & 2 \\2 & 0 & 1 \end{bmatrix}$$ Which is the bottom-left matrix. Doing this procedure to the right column gives you a matrix with the values of C.

Sorry for all the math jargon in my answer, if it caused any trouble.