若\( A \)是正交矩阵，则\( \left| A \right| = 1 \)或\( \left| A \right| = - 1 \) .
举一反三
- 若\(A\)是正交矩阵，则\(\left| A \right| = 1\).
- 若\(A\)是正交矩阵，则\(\left| A \right| = 1\).
- 若\(A\)是正交矩阵，则\(\left| A \right| = 1\).
- 设 \( A \)是 \( 3 \times 3 \)矩阵， \( B \)是 \( 4 \times 4 \)矩阵，且\( \left| A \right| = 1,\,\left| B \right| = - 2, \) 则\( \left| {\left| B \right|A} \right| = \) ______
- 设\( \left| { { x_0}} \right| = 4 \)，\( A \)为正交矩阵，则\( \left| {A{x_0}} \right| = \)______