(1) 交换两行的初等矩阵 E(i,j)

因为 E(i,j)E(i,j) = E

所以 E(i,j)^-1 = E(i,j)

(2) 第i行乘非零数k的初等矩阵 E(i(k))

因为 E(i(1/k))E(i(k)) = E

所以 E(i(k))^-1 = E(i(1/k))

(3) 第j行的k倍加到第i行的初等矩阵 E(i,j(k))

因为 E(i,j(-k))E(i,j(k)) = E

所以 E(i,j(k))^-1 = E(i,j(-k))