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:

• A. \( A \)
• B. \( 2A \)
• C. \( -A \)
• D. \( I - A \)

Hint:

When working with matrix identities, use known properties like \( A^2 = A \) to simplify expressions and check the validity of the given options.

Answer 1

The Correct Option is A

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 \( A \).