### Pick the Size of the Matrices

 2 rows 3 rows 4 rows 5 rows 6 rows 2x2 2x3 2x4 2x5 2x6 3x2 3x3 3x4 3x5 3x6 4x2 4x3 4x4 4x5 4x6 5x2 5x3 5x4 5x5 5x6 6x2 6x3 6x4 6x5 6x6

### Basic Information

Definition: Let $$A=[a_{ij}]$$ and $$B=[b_{ij}]$$ be two matrices with the same size, say $$m \times n$$. The sum of $$A$$ and $$B$$, written $$A+B$$, is the matrix obtained by adding corresponding elements from A and B. ié:

$$A + B =$$ $\begin{bmatrix} a_{11}+b_{11} & a_{12}+b_{12} & \dots & a_{1n}+b_{1n}\\ a_{21}+b_{21} & a_{22}+b_{22} & \dots & a_{2n}+b_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ a_{m1}+b_{m1} & a_{m2}+b_{m2} & \dots & a_{mn}+b_{mn} \end{bmatrix}$
Few theorems that may facilitate calculations of matrix addition:
a) $$(A + B) + C = A + (B + C)$$;
b) $$A + 0 = 0 + A = A$$;
c) $$A + (-A) = (-A) + A = 0$$;
d) $$A + B = B + A$$.