Question

State, with reason, whether the following are true or false. A, B and C are matrices of order
$2\times 2.$
(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) $A^2-B^2=(A+B)(A-B)$
(viii) $(A-B{)}^2=A^2-2A.B+B^2$

Answer 1

(i) True.
Addition of matrices is commutative.
(ii) False.
Subtraction of matrices is commutative.
(iii) True.
Multiplication of matrices is associative.
(iv) True.
Multiplication of matrices is distributive over addition.
(v) True.
Multiplication of matrices is distributive over subtraction.
(vi) True.
Multiplication of matrices is distributive over subtraction.
(vii) False.
Laws of algebra for factorization and expansion are not applicable to matrices.
(viii) False.
Laws of algebra for factorization and expansion are not applicable to matrices.