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Q.
If $A=\left[a_{i j}\right]_{m \times n}$ and $a_{i j}=\left(i^{2}+j^{2}-i j\right)(j-i), n$ is odd, then which of the following is not the value of $\operatorname{Tr}( A )$ ?
Matrices
Solution:
As $a_{i j}=\left(i^{2}+j^{2}-i j\right)(j-i)$
$a_{j i}=\left(j^{2}+i^{2}-j i\right)(i-j)=-a_{i j}$
$\Rightarrow A$ is skew symmetric $\Rightarrow T_{r}( A )=0$
Also $|A|=0$