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Mathematics
If A and B are square matrices of order 3× 3, then which of the following is true?
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Q. If A and B are square matrices of order $ 3\times 3, $ then which of the following is true?
Rajasthan PET
Rajasthan PET 2009
A
$ AB=0\Rightarrow A=O $ or $ B=O $
B
$ det(2AB)=8\text{ (}detA)\text{ (}detB) $
C
$ {{A}^{2}}-{{E}^{2}}=(A+B)(A-B) $
D
$ det(A+B)=det(A)+det(B) $
Solution:
det (2AB) = 23 det[A] det[B] = 8 det[A] det[B]