If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Question

The statement are True or False:

If A, B and C are square matrices of same order, then AB = AC always implies that B = C.

Answer 1

False

∵ If AB = AC => B=C

The above condition is only possible if matrix A is invertible

(i.e |A|≠0).

⇒ If A is invertible, then

⇒ A^-1(AB)= A^-1(AC)

⇒ (A^-1A)B = (A^-1A)C

⇒ IB=IC

⇒ B=C