求所有与A可交换的矩阵,只能用待定系数法么?比如说A=110011001A=110，011，001三阶矩阵，能看懂吧

Question

求所有与A可交换的矩阵,只能用待定系数法么?比如说A=1 1 0 0 1 1 0 0 1
A=110，011，001三阶矩阵，能看懂吧

Answer 1

设 B =
[ b11, b12, b13]
[ b21, b22, b23]
[ b31, b32, b33]
且 AB=BA, 即 AB-BA=0.
而 AB-BA =
[ b21, b22 - b11, b23 - b12]
[ b31, b32 - b21, b33 - b22]
[ 0, -b31, -b32]
所以 b11=b22=b33, b12=b23, b21=b31=b32=0
故 B =
a b c
0 a b
0 0 a