y Short Answer
If A = [aij] is a 2 * 2 matrix such that aij=i2-j21 - then write A
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If A=[a
ij
] is a square matrix such that a
ij
=i
2
−j
2
, then write whether A is symmetric or skew-symmetric.
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ANSWER
Given for A=[a
ij
] being a square matrix such that a
ij
=i
2
−j
2
.
Now a
ii
=i
2
−i
2
=0 and a
ji
=j
2
−i
2
=−(i
2
−j
2
)=−a
ij
.
So a
ji
=−a
ij
for i
=j and a
ii
=0 for all i,j.
This gives A
T
=−A.
So A is a skew-symmetric matrix.
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