i hope you can help i am soooo stuck here goes:


A= 0 1	B= 1 1	c= 2 5
   0 2	   3 4	   3 4
A,B and c are matrices

Evaluate AB and Ac (which I can do)


I need to prove that if the matrix A is inverible and AB =AC, then B = C. Why does this not contradict what happened in part a)?

thanking you

Hi Vikki,

If A is invertible and AB=AC then B=C.

This is true because if A is invertible,╩you multiply both sides of the equation AB=AC from the left by A inverse to get IB=IC which simplifies to B=C since╩I is the identity matrix.

This does not contradict what you did in part (a) (where AB=AC but B does not equal C) because the matrix A in your problem is not invertible (because of the column of zeroes). The words "if A is invertible"╩are very important in the statement underlined above.


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