行列式の展開

,

1.1

\(|A B|=|A||B|=|B||A|\)

1.2

\(\left|\begin{array}{ll}
A & B \\
O & D
\end{array}\right| \text { または }\left|\begin{array}{ll}
A & O \\
C & D
\end{array}\right|=|A||D|\)

1.3

\(\left|\begin{array}{cccc}
a_{11} & \cdots & \cdots & a_{1 n} \\
& a_{22} & & \vdots \\
& & \ddots & \vdots \\
O & & & a_{n n}
\end{array}\right|=\left|\begin{array}{cccc}
a_{11} & & & O \\
\vdots & a_{22} & & \\
\vdots & & \ddots & \\
a_{n 1} & \cdots & \cdots & a_{n n}
\end{array}\right|=a_{11} a_{22} \cdots a_{n n}\)

1.4

\(\left|\begin{array}{ll}
A & B \\
B & A
\end{array}\right|=|A+B||A-B|\)