Q.Write the order of each of the following matrices and state whether each is a row matrix, column matrix, square matrix, diagonal matrix, scalar matrix, unit (identity) matrix or null matrix:

Classifying a matrix means first counting its rows and columns to get the order, then checking the pattern of its entries against each type's definition.

1. $P$ has $1$ row and $3$ columns, so its order is $1\times3$. A matrix with exactly one row is by definition a row matrix.
2. $Q$ has $3$ rows and $1$ column, order $3\times1$ — a column matrix.
3. $R=\begin{pmatrix}4&0\\0&4\end{pmatrix}$ has $2$ rows and $2$ columns, order $2\times2$, so it is a square matrix. Its off-diagonal entries are both $0$, so it is also a diagonal matrix; and its diagonal entries ($4,4$) are equal, so it further qualifies as a scalar matrix.
4. $S=\begin{pmatrix}1&0\\0&1\end{pmatrix}$ is order $2\times2$, diagonal, and its diagonal entries are both $1$ — the defining property of the unit (identity) matrix $I_2$.
5. $T=\begin{pmatrix}0&0\\0&0\end{pmatrix}$ is order $2\times2$ with every entry $0$, so it is the null matrix $O$. Independent check: re-reading each matrix entry by entry against the definitions in Section 1 (row count, column count, position and value of zero/non-zero entries) confirms every classification above without any arithmetic to go wrong — a matrix's type is read directly off its shape and pattern, so the check is simply re-verifying the pattern-matching was done correctly, which it was.
   ✓Final answer

   P: $1\times3$ row matrix. Q: $3\times1$ column matrix. R: $2\times2$ diagonal and scalar matrix. S: $2\times2$ unit (identity) matrix. T: $2\times2$ null matrix.

Calling any diagonal matrix a scalar matrix (a diagonal matrix is only scalar if ALL diagonal entries are equal — a matrix like $\begin{pmatrix}2&0\\0&5\end{pmatrix}$ is diagonal but not scalar). Also confusing order notation: order is always written rows $\times$ columns, never the other way round.