If A is symmetric and B is skew symmetric matrix, then which of the following is/are correct?
A
ABAT is skew symmetric matrix
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B
ABT+BAT is symmetric matrix
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C
(A+B)(A−B) is symmetric
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D
(A+I)(B−I) is skew symmetric
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Solution
The correct options are AABAT is skew symmetric matrix BABT+BAT is symmetric matrix D(A+B)(A−B) is symmetric AT=A and BT=−B (A) (ABAT)T=ATTBTAT=−(ABAT)