Class CBSE Class 12 Mathematics Matrices and Determinants Q #758
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If \(A=\begin{bmatrix}1&2&3\\ -4&3&7\end{bmatrix}\) and \(B=\begin{bmatrix}4&3\\ -1&2\\ 0&5\end{bmatrix},\) then the correct statement is:
(A) Only AB is defined.
(B) Only BA is defined.
(C) AB and BA, both are defined.
(D) AB and BA, both are not defined.
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AI Tutor Explanation

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Step-by-Step Solution

  1. Check if AB is defined:

    Matrix A is a 2x3 matrix, and matrix B is a 3x2 matrix. Since the number of columns in A (3) is equal to the number of rows in B (3), the product AB is defined.

  2. Check if BA is defined:

    Matrix B is a 3x2 matrix, and matrix A is a 2x3 matrix. Since the number of columns in B (2) is equal to the number of rows in A (2), the product BA is defined.

  3. Conclusion:

    Since both AB and BA are defined, the correct statement is (C).

Correct Answer: AB and BA, both are defined.

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply their understanding of matrix multiplication rules to determine whether the products AB and BA are defined.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of matrix multiplication and the conditions under which it is defined (number of columns of the first matrix must equal the number of rows of the second matrix).
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the student's understanding of a core concept taught in the textbook regarding matrix operations.

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