Question

y Short Answer
If A = [aij] is a 2 * 2 matrix such that aij=i2-j21 - then write A​

Answer 1

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.

MEDIUM

Help best friend

Study later

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.