Class CBSE Class 12 Mathematics Matrices and Determinants Q #1489
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
A matrix B = $[b_{ij}]_{m \times m}$ is said to be a diagonal matrix, if :
(A) $b_{ij} = 0$, when $i = j$
(B) $b_{ij} = 1$, when $i = j$
(C) $b_{ij} = 1$, when $i \neq j$
(D) $b_{ij} = 0$, when $i \neq j$
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Correct Answer: D

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Detailed Solution

Step 1: Recall the definition of a diagonal matrix.

A diagonal matrix is a square matrix in which all the elements outside the main diagonal are zero. The elements on the main diagonal can be any value, including zero.

Step 2: Analyze the given options.

We need to find the condition that ensures all elements outside the main diagonal are zero.

Step 3: Evaluate option (A).

Option (A) states: $b_{ij} = 0$, when $i = j$. This means the elements on the main diagonal are zero. This is a special case of a diagonal matrix, but not the general definition.

Step 4: Evaluate option (B).

Option (B) states: $b_{ij} = 1$, when $i = j$. This means the elements on the main diagonal are one. This describes an identity matrix, which is a special case of a diagonal matrix, but not the general definition.

Step 5: Evaluate option (C).

Option (C) states: $b_{ij} = 1$, when $i \neq j$. This means all elements outside the main diagonal are one, which is not a diagonal matrix.

Step 6: Evaluate option (D).

Option (D) states: $b_{ij} = 0$, when $i \neq j$. This means all elements outside the main diagonal are zero, which is the definition of a diagonal matrix.

Final Answer: $b_{ij} = 0$, when $i \neq j$

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because the student needs to comprehend the definition of a diagonal matrix and apply it to the given options.
Knowledge Dimension: FACTUAL
Justification: The question directly tests the student's knowledge of the definition of a diagonal matrix.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question is a direct application of the definition provided in the textbook.
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