Class CBSE Class 12 Mathematics Matrices and Determinants Q #843
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
3. If A is a square matrix and $A^{2}=A$ then $(I+A)^{2}-3A$ is equal to :
(A) I
(B) A
(C) 2A
(D) 3I
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AI Tutor Explanation

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Step-by-Step Solution

We are given that $A^2 = A$. We need to find the value of $(I+A)^2 - 3A$.

First, expand $(I+A)^2$:

$(I+A)^2 = (I+A)(I+A) = I^2 + IA + AI + A^2 = I + A + A + A^2 = I + 2A + A^2$

Since $A^2 = A$, we can substitute this into the expression:

$(I+A)^2 = I + 2A + A = I + 3A$

Now, substitute this back into the original expression:

$(I+A)^2 - 3A = (I + 3A) - 3A = I + 3A - 3A = I$

Therefore, $(I+A)^2 - 3A = I$.

Correct Answer: I

AI Suggestion: Option A

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the given condition $A^2 = A$ and algebraic manipulation to simplify the expression.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure of expanding the expression and then simplifying it using the given condition.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the knowledge of matrix algebra and properties.

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