Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Algebra

Question:

An identity matrix can be written as $[a_{ij}]_{n×n}$ where,

Options:

$aij=\left\{\begin{matrix}0, & when & i≠j \\k, & when & i=j \end{matrix}\right.$

$aij=\left\{\begin{matrix}0, & when & i≠j \\1, & when & i=j \end{matrix}\right.$

$aij=\left\{\begin{matrix}k, & when & i≠j \\0, & when & i=j \end{matrix}\right.$

$aij=\left\{\begin{matrix}1, & when & i≠j \\0, & when & i=j \end{matrix}\right.$

Correct Answer:

$aij=\left\{\begin{matrix}0, & when & i≠j \\1, & when & i=j \end{matrix}\right.$

Explanation:

The correct answer is Option (2) → $aij=\left\{\begin{matrix}0, & when & i≠j \\1, & when & i=j \end{matrix}\right.$

Identity matrix = $aij=\left\{\begin{matrix}0, & when & i≠j \\1, & when & i=j \end{matrix}\right.$

Only diagonal elements are not zero.