Previous Year NEET Question- Matrices

Question: If $A$ and $B$ are two matrices such that $A^2 = B^2$ and $A + B = \begin{bmatrix} 2 & 2 \ 0 & 2 \end{bmatrix}$, then $A - B$ is equal to (A) $\begin{bmatrix} 0 & 0 \ 0 & 0 \end{bmatrix}$ (B) $\begin{bmatrix} 1 & 1 \ 0 & 1 \end{bmatrix}$ (C) $\begin{bmatrix} 1 & -1 \ 0 & 1 \end{bmatrix}$ (D) $\begin{bmatrix} -1 & 1 \ 0 & -1 \end{bmatrix}$

Answer: (D)

Explanation:

We have $A^2 = B^2$ and $A + B = \begin{bmatrix} 2 & 2 \ 0 & 2 \end{bmatrix}$.

Expanding $A^2$ and $B^