If A and B are symmetric then write the condition for AB is also symmetric
Rishu , 6 Years ago
Grade 12
Algebra> If A and B are symmetric then write the c...
1 Answers
Arun
Last Activity: 6 Years ago
Dear student
Since AB is symmetric, we have AB = (AB)T
But (AB)T = BT AT
Hence AB = BT AT …(1)
It is also given that A and B are symmetric
AT = A and BT = B
Hence (1) becomes, AB = BA
Thus AB is symmetric if and only if AB = BA. Or A and B are commute.
But (AB)T = BT AT
Hence AB = BT AT …(1)
It is also given that A and B are symmetric
AT = A and BT = B
Hence (1) becomes, AB = BA
Thus AB is symmetric if and only if AB = BA. Or A and B are commute.
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