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CBSE Class 12 Math 2026 All Sets Solved Paper

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Question : 6 of 20
Marks: +1, -0
If A and B are skew symmetric matrices of same order, then which of the following matrices is also skew symmetric?
Solution:  
A and B are skew symetric matrix
AT=−AA^{T}=-A
BT=−BB^{T}=-B
(A) (AB)T=BTAT=BA(AB)^{T}=B^{T}A^{T}=BA
(B) (AB+BA)T=(AB)T+(BA)T(AB+BA)^{T}=(AB)^{T}+(BA)^{T}
=BTAT+ATBT=B^{T}A^{T}+A^{T}B^{T}
=BA+AB=BA+AB
=AB+BA=AB+BA
(C) ((A+B)2)T=(AT+BT)2((A+B)^{2})^{T}=(A^{T}+B^{T})^{2}
=(−A−B)2=(-A-B)^{2}
=(A+B)2=(A+B)^{2}
(D) (A−B)T=AT−BT(A-B)^{T}=A^{T}-B^{T}
=−A+B=-A+B
=−(A−B)=-(A-B)
⇒(A−B)\Rightarrow(A-B) is a skew symmetric matrix.
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