Q32 of 146 Page 52

Let and a = 4, b = –2.
Show that:

A + (B + C) = (A + B) + C

Given A = B = and C =

LHS = A + (B + C) =

⇒ LHS =

RHS = (A + B) + C =

⇒ RHS =

Clearly LHS = RHS =

Hence,

A + (B + C) = (A + B) + C …proved

Let A and B be square matrices of the order 3 × 3. Is (AB)² = A²B² ? Give reasons.

Show that if A and B are square matrices such that AB = BA, then (A + B)² = A² + 2AB + B².

Let and a = 4, b = –2.

Show that:

A(BC) = (AB)C

Let and a = 4, b = –2.

Show that:

(a + b)B = aB + bB

Let and a = 4, b = –2.Show that:A + (B + C) = (A + B) + C