MatricesMedium
Question
Which of the following statement(s) is true about two square matrices A & B of same order -
Options
A.AB is symmetric ⇒ (AB)2 is symmetric
B.AB′ is symmetric ⇒ BA′ - AB′ is symmetric
C.Trace (BA′ + AB′) = 0
D.AB and AB′ both are symmetric ⇒ (B′ - B)A′ = A(B - B′)
Solution
(AB′)′ = BA′ ⇒ AB′ = BA′ ⇒ BA′ - AB′ = 0
(AB)′ = AB ⇒ B′A′ = AB & (AB′)′ = AB′ ⇒ BA′ = AB′
Subtracting (B′ - B)A′ = A(B′ - B)A′ = A(B - B′)
(AB)′ = AB ⇒ B′A′ = AB & (AB′)′ = AB′ ⇒ BA′ = AB′
Subtracting (B′ - B)A′ = A(B′ - B)A′ = A(B - B′)
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