If A, B, C are three non zero square matrices of same order, find the condition on A such that - Maths - Matrices

Question

If A, B, C are three non zero square matrices of same order,
find the condition
on A such that AB = AC implies B = C

Pronay · Accepted Answer

If A is invertible and AB=AC, then B=C is true Proof: AB = AC (given) Multiplying both sides by $A^{- 1}$ , we get $A^{- 1}$ AB = $A^{- 1}$ AC We know, $A^{- 1}$ A = I So, IB = IC OR, B=C

If A, B, C are three non zero square matrices of same order, find the conditionon A such that AB = AC implies B = C.

If A, B, C are three non zero square matrices of same order, find the condition
on A such that AB = AC implies B = C.