Class CBSE Class 12 Mathematics Matrices and Determinants Q #842
KNOWLEDGE BASED
UNDERSTAND
1 Marks 2023 MCQ SINGLE
2. The product $\begin{bmatrix}a & b\\ -b & a\end{bmatrix}\begin{bmatrix}a & -b\\ b & a\end{bmatrix}$ is equal to :
(A) $\begin{bmatrix}a^{2}+b^{2} & 0\\ 0 & a^{2}+b^{2}\end{bmatrix}$
(B) $\begin{bmatrix}(a+b)^{2} & 0\\ (a+b)^{2} & 0\end{bmatrix}$
(C) $\begin{bmatrix}a^{2}+b^{2} & 0\\ a^{2}+b^{2} & 0\end{bmatrix}$
(D) $\begin{bmatrix}a & 0\\ 0 & b\end{bmatrix}$
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Step-by-Step Solution

Let's multiply the two matrices:

$\begin{bmatrix}a & b\\ -b & a\end{bmatrix}\begin{bmatrix}a & -b\\ b & a\end{bmatrix} = \begin{bmatrix}a*a + b*b & a*(-b) + b*a\\ -b*a + a*b & -b*(-b) + a*a\end{bmatrix}$

Simplifying the resulting matrix:

$\begin{bmatrix}a^{2}+b^{2} & -ab + ab\\ -ab + ab & b^{2} + a^{2}\end{bmatrix} = \begin{bmatrix}a^{2}+b^{2} & 0\\ 0 & a^{2}+b^{2}\end{bmatrix}$

Correct Answer: $\begin{bmatrix}a^{2}+b^{2} & 0\\ 0 & a^{2}+b^{2}\end{bmatrix}$

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AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an UNDERSTAND question because it requires the student to understand the process of matrix multiplication and apply it to the given matrices.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a specific procedure, namely matrix multiplication, to arrive at the correct answer.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of matrix multiplication as covered in the textbook.

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