Class CBSE Class 12 Mathematics Matrices and Determinants Q #738
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2024 MCQ SINGLE
If \(A=[a_{ij}]\) is an identity matrix, then which of the following is true ?
(A) \(a_{ij}=\begin{cases}0,&if~i=j\\ 1,&if~i\ne j\end{cases}\)
(B) \(a_{ij}=1,\forall i,j\)
(C) \(a_{ij}=0,\forall i,j\)
(D) \(a_{ij}=\begin{cases}0,&if~i\ne j\\ 1,&if~i=j\end{cases}\)
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Step-by-Step Solution

An identity matrix is a square matrix in which all the elements of the principal diagonal are ones and all other elements are zeros.

This can be expressed as:

\(a_{ij} = \begin{cases} 0, & \text{if } i \ne j \\ 1, & \text{if } i = j \end{cases}\)

Correct Answer: \(a_{ij}=\begin{cases}0,&if~i\ne j\\ 1,&if~i=j\end{cases}\)

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires the student to recall and explain the definition of an identity matrix.
Knowledge Dimension: FACTUAL
Justification: The question directly tests the student's knowledge of the definition of an identity matrix, which is a factual piece of information.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. It directly assesses recall of a definition from the textbook.

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