Question:
Choose the most appropriate option.
If \( A \) is a square matrix such that \( A^2 = A \) and \( B = I \), then \( AB + BA + I - (I - A)^2 \) is equal to:
Choose the most appropriate option.
If \( A \) is a square matrix such that \( A^2 = A \) and \( B = I \), then \( AB + BA + I - (I - A)^2 \) is equal to:
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When working with matrix identities, use known properties like \( A^2 = A \) to simplify expressions and check the validity of the given options.
Updated On: Apr 1, 2025
- \( A \)
- \( 2A \)
- \( -A \)
- \( I - A \)
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The Correct Option is A
Solution and Explanation
Given that \( A^2 = A \) and \( B = I \), we substitute these into the expression:
\[
AB + BA + I - (I - A)^2.
\]
Simplify the terms to find that the result is equal to \( A \).
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