A) \[4\sqrt{2}\]
B) \[2\sqrt{2}\]
C) 8
D) \[8\sqrt{2}\]
Correct Answer: D
Solution :
Since, A is skew symmetric matrix \[\therefore \] \[{{A}^{T}}=-A\] Now,\[{{({{B}^{T}}AB)}^{T}}={{B}^{T}}{{A}^{T}}{{({{B}^{T}})}^{T}}\](By reversal law) \[={{B}^{T}}{{A}^{T}}B\] \[[\because {{({{B}^{T}})}^{T}}=B]\] \[={{B}^{T}}(-A)B\] \[=-{{B}^{T}}AB\] \[(\because {{A}^{T}}=-A)\] Hence,\[{{B}^{T}}AB\]is skew symmetric matrix.
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