If A and B are two non-zero $n \times n$ matrices such that $A^2 + B = A^2 B$, then
Step-by-Step Solution
Key Concept: Rearrange the equation to factor and use properties of identity matrix
From $A^2 + B = A^2B$: $A^2 - A^2B + B = 0 \Rightarrow A^2(I - B) = -B \Rightarrow A^2(B-I) = B$. Also rearranging: $A^2 + B = A^2B \Rightarrow A^2 = A^2B - B = B(A^2 - I) \Rightarrow A^2 = BA^2 - B$. Adding original: $A^2 + B = A^2B$ and $A^2 = BA^2 - B$ gives $A^2B = BA^2$. Answer: (4)
Correct Answer: $A^2B = BA^2$