${\mathit{S}}_{\mathbf{1}}\mathbf{:}$ The matrix $B^T$ AB is symmetric or skew-symmetric according as A is symmetric or skew-symmetric matrix.
${\mathit{S}}_{\mathbf{2}}\mathbf{:}$ If A and B are symmetric matrices of the same order then $AB-BA$ is a symmetric matrix.
${\mathit{S}}_{\mathbf{3}}\mathbf{:}$ Null matrix of order $n\times n$  satisfies both the symmetric and skew-symmetric property
Then the number of statements which are true: