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A 2 − B 2 = (A − B) (A + B)
⇐⇒ A 2 − B 2 = A 2 + AB − BA − B 2
⇐⇒ BA = AB (A B )
¡ ¨ A =
¨¥ ¨ ¡ £¢
AB =
0 1
0 1
B =
(A + B) 2 = A 2 + 2AB + B 2
A 2 − B 2 = (A − B) (A + B)
BA =
0 1
0 1
−1 −1
0 0
−1 −1
0 0
0 1
0 1
=
=
0 0
0 0
0 −2
0 0
AB BA ¥¤
=
(A + B) 2 = A2 + 2AB + B2 A 2 − B 2 = (A − B) (A + B)
−1 −1
0 0
¡ ¨ A B 2×2
E 2 × 2 (E) = 0
λ E 2 = λ I2
(AB − BA) = 0
¥¤
A B ¢ C 2 2
£¢
×
¨¥ ¨ A =
(AB − BA) 2 C = C (AB − BA) 2
a11 a12
a21 a22
B =
b11 b12
b21 b22