9. a) Prove that ifA is invertible and AB-AC then B = C.

Question

Question

math algebra

Answer 1

Answer #1

By given condition

AB=AC

Multiply both sides by A- (A inverse)

A^-¹AB= A^-1AC. 1)

But AA^-1=I

Where I is a unit matrix

So equation 1) becomes

IB=IC

According to rule if we multiy any matrix by I i.e unit matrix we get same matrix

B=C

Hence proved

Answer 2

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