Question

Unit matrix is a diagonal matrix in which all the diagonal elements are unity. Unit matrix of order ${}^{\prime }{n}^{\prime }$ is denoted by $I_n\left(orI\right)$ i.e. $A=[a_{ij}{]}_n$ is a unit matrix when $a_{ij}=0$ for $i\ne jand{a}_{ij}=1$ for $i==$.

• A. True
• B. False

Answer 1

The correct option is A True

Unit matrix is a diagonal matrix in which all the diagonal elements is $1$ and rest of the elements are $0$

$I_n={\left[\begin{array}{ccccc}1& 0& 0& .....& 0\\ 0& 1& .....& .....& 0\\ .& .& .& & .\\ .& .& .& & .\\ 0& 0& ....& .....& 1\end{array}\right]}_{n\times n}A={\left[a_{ij}\right]}_n={\left[\begin{array}{cccc}{a}_{11}& a_{12}& .....& a_{1n}\\ a_{21}& a_{22}& .....& a_{2n}\\ .& & & \\ .& & & \\ a_{n1}& a_{n2}& .....& a_{nn}\end{array}\right]}_{n\times n}$

this becomes unit matrix $In$ when $a_{11},a_{22}.......a_{nn}$ elements are $1$ and rest of the elements are $0$.

$A={\left[a_{ij}\right]}_n$ is a unit matrix

When $a_{ij}=0$ for $i\ne j$

$=1$ when $i=j$