Class CBSE Class 12 Mathematics Matrices and Determinants Q #754
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2025 MCQ SINGLE
Let both \(AB^{\prime}\) and \(B^{\prime}A\) be defined for matrices A and B. If order of A is \(n\times m\), then the order of B is:
(A) \(n\times n\)
(B) \(n\times m\)
(C) \(m\times m\)
(D) \(m\times n\)
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AI Tutor Explanation

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Step-by-Step Solution

Let the order of matrix A be \(n \times m\). This is given.

Let the order of matrix B be \(p \times q\).

For \(AB'\) to be defined, the number of columns of A must be equal to the number of rows of \(B'\). Since B is \(p \times q\), \(B'\) is \(q \times p\). Therefore, \(m = q\).

For \(B'A\) to be defined, the number of columns of \(B'\) must be equal to the number of rows of A. Therefore, \(p = n\).

So, the order of B is \(p \times q = n \times m\).

Correct Answer: \(n\times m\)

AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires students to comprehend the conditions for matrix multiplication to be defined and apply that understanding to determine the order of matrix B.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of matrix multiplication and the compatibility of matrix orders for the multiplication to be defined.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of matrix algebra concepts as covered in the textbook.

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