Polynomial Addition:

(1 + 2x - 3x^2) + (2 - x) = 3 + x - 3x^2

Polynomial Multiplication:

(1 + x^10000)(1 + 2x^10000) = 1 + 2x^10000 + 2x^20000

Matrix Addition:

 1  3 -4      8  3  0      9  6 -4
 1  1 -2  +   3 10  2  =   4 11  0
-1 -2  5      0  2  6     -1  0 11

Matrix Multiplication:

 1  3 -4      8  3  0     17  25 -18
 1  1 -2  x   3 10  2  =  11   9 -10
-1 -2  5      0  2  6    -14 -13  26