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  • Which of the following is correct for Identity Matrix I of order m x n?Option: 1 Identity matrix I is always square matrix.<div class='

Which of the following is correct for Identity Matrix I of order m x n?

Option: 1

Identity matrix I is always square matrix.


Option: 2

\mathrm{a}_{\mathrm{ij}}=\left\{\begin{array}{ll}{0,} & {i \neq j} \\ {1,} & {i=j}\end{array}\right.


Option: 3

m=n


Option: 4

All of the above


Answers (1)

best_answer

 

 

Unit or Identity Matrix: A diagonal matrix of order n whose all the diagonal elements are equal to one is called an identity matrix of order n. It is represented as I.

So, a square matrix \mathrm{A}=\left[\mathrm{a}_{\mathrm{ij}}\right]_{ \mathrm{n} \times \mathrm{n}} is Identity matrix if 

\mathrm{a}_{\mathrm{ij}}=\left\{\begin{array}{ll} 0, & i \neq j \\ 1, & i=j \end{array}\right.

For example,

\mathrm{I}_{3}=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]


 

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An identity matrix is defined as a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros. The effect of multiplying a given matrix by an identity matrix is to leave the given matrix unchanged.

 

Hence all the options are correct

Posted by

Pankaj

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