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Let A, B, and C be square matrices of order n overR. Prove that if A.pdf

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Let A, B, and C be square matrices of order n overR. Prove that if A is invertible and AB = AC thenB = C. Solution given that A is invertible, by definition AA-1 = I= A-1A, here I denote the identity matrix andA- 1 denote the inverse of A consider AB = AC multiply on both sides with A-1 from left, wehave A-1(AB) = A-1(AC) (A-1A)B = (A-1A)C IB = IC implies B = C.

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Let A, B, and C be square matrices of order n overR. Prove that if A is invertible and AB = AC thenB = C. Solution given that A is invertible, by definition AA-1 = I= A-1A, here I denote the identity matrix andA- 1 denote the inverse of A consider AB = AC multiply on both sides with A-1 from left, wehave A-1(AB) = A-1(AC) (A-1A)B = (A-1A)C IB = IC implies B = C

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Let A, B, and C be square matrices of order n overR. Prove that if A.pdf

  • 1. Let A, B, and C be square matrices of order n overR. Prove that if A is invertible and AB = AC thenB = C. Solution given that A is invertible, by definition AA-1 = I= A-1A, here I denote the identity matrix andA- 1 denote the inverse of A consider AB = AC multiply on both sides with A-1 from left, wehave A-1(AB) = A-1(AC) (A-1A)B = (A-1A)C IB = IC implies B = C