解: (A,E) =
111100
2 -11010
120001
r2-2r1,r3-r1
111100
0 -3 -1 -210
01 -1 -101
r1-r3,r2+3r3
10220 -1
00 -4 -513
01 -1 -101
r2*(-1/4),r1-2r2,r3+r2
100 -1/21/21/2
0015/4 -1/4 -3/4
0101/4 -1/41/4
r2<->r3
100 -1/21/21/2
0101/4 -1/41/4
0015/4 -1/4 -3/4
A^-1 =
-1/21/21/2
1/4 -1/41/4
5/4 -1/4 -3/4