Suppose that A B C D are square matrices and I is the identi

Suppose that A, B, C, D are square matrices and I is the identity matrix of the same size.

(a) Show that if AB = AC and DA = I, then B = C.

(b) Show that if AC = BC and CD = I, then A = B.

(c) Show that if AB = I and CA = I, then B = C.

given AB= I

so B=A^-1....................(i)

given CA=I

so C=A^-1....................(ii)

from (i),(ii)

we can say that B=C

therefore B=C