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.

(i) A + B = B + A

The above statement is true because addition of matrices is commutative.

(ii) A - B = B - A

The above statement is false because subtraction of matrices is not commutative.

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

The above statement is true because multiplication of matrices is associative.

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

The above statement is true because multiplication of matrices is distributive over addition.

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

The above statement is true because multiplication of matrices is distributive over subtraction.

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

The above statement is true because multiplication of matrices is distributive over subtraction.

(vii) A² - B² = (A + B)(A - B)

The above statement is false because laws of algebra for factorization and expansion are not applicable to matrices.

(viii) (A - B)² = A² - 2A.B + B²

The above statement is false because laws of algebra for factorization and expansion are not applicable to matrices.