Q.Write definition of scalar matrix.

The matrix has 2 rows and 4 columns, so its order is $2\times 4$ — option (iv).

Concept. For a matrix, the order is written as $(\text{rows})\times(\text{columns})$.

Steps.

• $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & 5 & 12 \end{bmatrix}$.
• Count the horizontal lines (rows): there are $2$. …

A column matrix has a single column.

A matrix of order $m\times1$ (one column, any number of rows) is call …

Scalar matrix = diagonal matrix with all equal diagonal entries.

A square matrix $A = [a_{ij}]$ is called a scalar matrix if:

1. It is a diagonal matrix, i.e. $a_{ij} = 0$ for all $i\ne j$ (all off-diagonal entries are zero), AND
2. All the diagonal entries are equal, i.e. $a_{11}=a_{22}=\cdots=a_{nn}=k$ for some fixed scalar $k$. …

A matrix $A=[a_{ij}]_{m\times n}$ is called a column matrix when it has only one column, i.e. $n=1$.

By definition, a column matrix (or column vector) has $m$ rows but a single column, so its order is $m\times 1$. This means the …

An identity matrix has 1’s on the main diagonal and 0’s everywhere else. The correct description is option (D).

A column matrix has exactly one column and any number of rows — order $m\times1$.

…

An identity matrix has 1's on the main diagonal and 0's everywhere else.

The $3\times 3$ identity matrix is $I_3=\begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}$. …

The $3\times3$ identity matrix is $\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$.

A unit (identity) matrix $I$ is a square matrix whose diagonal entries are all $1$ and every off-diagonal entry is $0$. It satisfies $AI=IA=A$. O …