A scalar matrix has all diagonal elements equal to the same value, with zeros elsewhere. In our matrix, all diagonal elements are 1 and all off-diagonal elements are 0, so it is a scalar matrix.
A diagonal matrix has non-zero elements only on the main diagonal. Hence, it is also a diagonal matrix.
A skew-symmetric matrix satisfies AT=−A.
The transpose of our matrix is itself: 100010001
The negative of our matrix is: −1000−1000−1
Since the transpose ≠ negative, it is not skew-symmetric.
A symmetric matrix satisfies AT=A.
Since the transpose equals the original matrix, it is symmetric.