Given $\mathbf{P}$ is $m \times n$ matrix, $\mathbf{Q}$ is $n \times l$ matrix, $\mathbf{R}$ and $\mathbf{S}$ are $n \times n$ matrices, and superscript $\mathrm{T}$ denotes transpose. Consider
Relationship $1$: $(\mathbf{P Q})^{\mathrm{T}}=\mathbf{Q}^{\mathrm{T}} \mathbf{P}^{\mathrm{T}}$
Relationship $2$: $(\mathbf{R S})^{\mathrm{-1}}=\mathbf{S}^{\mathrm{-1}} \mathbf{R}^{\mathrm{-1}}$
Which one of the following is correct?
- Relationship $1$ is false; Relationship $2$ is false
- Relationship $1$ is true; Relationship $2$ is false
- Relationship $1$ is true; Relationship $2$ is true
- Relationship $1$ is false; Relationship $2$ is true
