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Question

IfA, B are symmetric matrices of the same order then ABBA is

A
symmetric matrix
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B
skew symmetric matrix
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C
Diagonal matrix
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D
identity matrix
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Solution

The correct option is B skew symmetric matrix
Let A=[accl]
B=[dffe]
AB=[(ad+cf)(af+ce)(cd+lf)(cf+le)]
BA=[(da+fc)(dc+lf)(fa+ce)(fc+le)]
ABBA=[0af+ce(dc+lf)[(af+ce)(dc+lf)]0]
skew symmetric matrix.

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