Determinants Matrices Question 142
Question: If A is symmetric as well as skew-symmetric matrix, then A is
Options:
A) Diagonal
B) Null
C) Triangular
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] Let $ A={{[a _{ij}]} _{n\times m}} $ . Since A is skew-symmetric $ a _{ii}=0 $ (i = 1, 2,–…….n) and $ a _{ji}=-a _{ji}(i\ne j) $ Also, A is symmetric so $ a _{ji}=-a _{ji}\forall $ i and j
$ \therefore a _{ji}=0\forall i\ne j $ Hence $ a _{ij}=0\forall $ i and $ j\Rightarrow A $ is a null zero matrix
BETA
