State, with reason, whether the following are true or false. A, B and C are matrices of order 2 × 2.

(i) A + B = B + A

(ii) A - B = B - A

(iii) (B.C).A = B.(C.A)

(iv) (A + B).C = A.C + B.C

(v) A.(B - C) = A.B - A.C

(vi) (A - B).C = A.C - B.C

(vii) A² - B² = (A + B)(A - B)

(viii) (A - B)² = A² - 2A.B + B².

If a matrix A = $\begin{bmatrix$}[r] 0 & 1 \ 2 & -1 \end{bmatrix} and matrix B = $\begin{bmatrix$}[r] 3 \ 1 \end{bmatrix}, then which of the following is possible :

1. A + B

2. A - B

3. AB

4. BA

If $\begin{bmatrix$}[r] 2x - y \ x + y \end{bmatrix} = \begin{bmatrix}[r] 9 \ 9 \end{bmatrix}, the value of x and y are :

1. x = 3 and y = 3

2. x = 3 and y = 9

3. x = 3 and y = 6

4. x = 6 and y = 3

If matrix A = $\begin{bmatrix$}[r] x - y & x + y \ y - x & y + x \end{bmatrix} and matrix B = $\begin{bmatrix$}[r] x + y & y - x \ x - y & y + x \end{bmatrix}, then A + B is :

1. $\begin{bmatrix$}[r] 2y & 2x \ 0 & 2(x + y) \end{bmatrix}

2. $\begin{bmatrix$}[r] 2x & 2(x + y) \ 0 & 0 \end{bmatrix}

3. $\begin{bmatrix$}[r] 2x & 2y \ 0 & 2(x + y) \end{bmatrix}

4. $\begin{bmatrix$}[r] 2x - 2y & 2y \ 0 & 0 \end{bmatrix}