Let A and B be \[3\times 3\] matrices of real numbers, where A is symmetric, B is skew symmetric, and \[(A+B)(A-B)=(A-B)(A+B).\] If \[{{(AB)}^{t}}={{(-1)}^{k}}AB\]where \[{{(AB)}^{t}}\] is the transpose of the matrix AB, then k is

Let A and B be \[3\times 3\] matrices of real numbers, where A is symm

1.	Let A and B be \[3\times 3\] matrices of real numbers, where A is symmetric, B is skew symmetric, and \[(A+B)(A-B)=(A-B)(A+B).\] If \[{{(AB)}^{t}}={{(-1)}^{k}}AB\]where \[{{(AB)}^{t}}\] is the transpose of the matrix AB, then k is
A.	Any integer
B.	Odd integer
C.	Even integer
D.	Cannot say anything
Answer» C. Even integer

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Let A and B be \[3\times 3\] matrices of real numbers, where A is symmetric, B is skew symmetric, and \[(A+B)(A-B)=(A-B)(A+B).\] If \[{{(AB)}^{t}}={{(-1)}^{k}}AB\]where \[{{(AB)}^{t}}\] is the transpose of the matrix AB, then k is

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