Assume $X$, $Y$, $Z$, $W$, and $P$ are matrices of order $2 \times n$, $3 \times k$, $2 \times p$, $n \times 3$, and $p \times k$ respectively:

> 
> $$X = \begin{pmatrix} a\_{11} & a\_{12} & \ldots & a\_{1n}\\ a\_{21} & 
>  a\_{22} & \ldots & a\_{2n}\\ \end{pmatrix} $$
> 
> 
> 

---

> 
> $$Y = 
> \begin{pmatrix}
> a\_{11} & a\_{12} & \ldots & a\_{1k}\\
> a\_{21} & a\_{22} & \ldots & a\_{2k}\\
> a\_{31} & a\_{32} & \ldots & a\_{3k}\\
> \end{pmatrix}
> $$
> 
> 
> 

---

> 
> $$Z = \begin{pmatrix} a\_{11} & a\_{12} & \ldots & a\_{1p}\\ a\_{21} & a\_{22} & \ldots & a\_{2p}\\ \end{pmatrix} $$
> 
> 
> 

---

> 
> $$W= \begin{pmatrix} a\_{11} & a\_{12} & a\_{13}\\ a\_{21} & a\_{22} & a\_{23}\\ \vdots & \vdots & \vdots\\ a\_{n1} & a\_{n2} &
> a\_{n3} \end{pmatrix} $$
> 
> 
> 

---

> 
> $$P = \begin{pmatrix} a\_{11} & \ldots & a\_{1k}\\ a\_{21} & \ldots & a\_{2k}\\ \vdots & \vdots & \vdots\\ a\_{p1} &\ldots & a\_{pk}
> \end{pmatrix} $$
> 
> 
> 

---

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Now, the questions:

Q1. What will be the restrictions on $n$, $k$, and $p$ so that $PY + WY$ will be defined?

Q2. If $n$ = $p$, then what is the order of the matrix $7X^2 - 5Z^3$?

Can the above said questions be solved using a logical approach? If so, please explain.