Question

Construct the matrix $A=[a_{ij}{]}_{3\times 3}$, where $a_{ij}=i-j$. Then $A$ is

• A. Diagonal matrix
• B. Skew-symmetric matrix
• C. Symmetric matrix
• D. Upper triangular matrix

Answer 1

The correct option is B Skew-symmetric matrix

So, the matrix $A$ with order $3\times 3$ is
$A=\left[\begin{array}{ccc}0& -1& -2\\ 1& 0& -1\\ 2& 1& 0\end{array}\right]-A=\left[\begin{array}{ccc}0& 1& 2\\ -1& 0& 1\\ -2& -1& 0\end{array}\right]$
Clearly $A^T=-A$
Hence, it is a skew-symmetric matrix.