A = [ a i j ] n × n and a i j = i 2 − j 2 then A is necessarily Options: A . &nbspa unit matrix B . &nbspsymmetric matrix C . &nbspskew symmetric matrix D . &nbspzero matrix

A=[aij]n×n and aij=i2−j2 then A is necessarily

Question

A = [a_{i j}]_{n \times n}

and

a_{i j} = i^{2} - j^{2}

then A is necessarily

Options:

A . a unit matrix

B . symmetric matrix

C . skew symmetric matrix

D . zero matrix

Answer: Option C
:
C

a_{j i} = j^{2} - i^{2} = - (i^{2} - j^{2}) = - a_{i j}

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