Class CBSE Class 12 Mathematics Matrices and Determinants Q #836
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If for a square matrix A, A² - A + I = O then A⁻¹ equals
(A) A
(B) A+I
(C) I-A
(D) A-I
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AI Tutor Explanation

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Step-by-Step Solution

Given: A² - A + I = O

We need to find A⁻¹.

Multiply the given equation by A⁻¹:

A⁻¹(A² - A + I) = A⁻¹O

A⁻¹A² - A⁻¹A + A⁻¹I = O

A - I + A⁻¹ = O

Now, isolate A⁻¹:

A⁻¹ = I - A

Correct Answer: I-A

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the properties of matrices and inverse matrices to solve the given equation and find the inverse of matrix A.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to manipulate the given matrix equation and isolate the inverse matrix. This involves algebraic manipulation and knowledge of matrix properties.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of matrix algebra concepts as covered in the textbook.

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