#덧셈

1) 교환법칙 $A + B = B + A$

2) 결합법칙 $(A + B) + C = A + (B + C)$

3) $A + 0 = A$, 영행렬은 0으로 채워진 행렬로, $A$와 같은 크기입니다

4) $(-A) + A = 0$

#스칼라 곱셈

1) $\lambda(A + B) = A \cdot \lambda + B \cdot \lambda$

2) $(\lambda + \mu) \cdot A = \lambda \cdot A + \mu \cdot B$

3) $(\lambda \cdot \mu) \cdot A = \lambda\cdot (\mu \cdot A);$

4) $A \cdot 1 = A$

#전치

1)$(A^T)^T = A$

2)$(A + B)^T = A^T + B^T$

3)$(A \cdot c)^T = A^T \cdot c$

#곱셈

1)$A \cdot (B + C) = A \cdot B + A \cdot C$

2)$(A \cdot B) \cdot C = A \cdot (B \cdot C)$

3)$A \cdot B \neq B \cdot A$

예시:

$A = \begin{pmatrix}

0& 1\\ 0& 0

\end{pmatrix}, B = \begin{pmatrix}

0& 0\\ 1& 0

\end{pmatrix}, A \cdot B = \begin{pmatrix}

1& 0\\ 0& 0

\end{pmatrix}, B \cdot A = \begin{pmatrix}

0& 0\\ 0& 1

\end{pmatrix}$