Proving B=C Given AB=BC and A Non-Singular

[nokia8650]

Given that AB = BC, and that A is non-singular, prove that B =C.

I don't know how to do matrices in these forums, so where I write a matrix, I mean (a,b,c,d)

Given that A = (3,6,1,2) and B = (1,5,0,1), find a matrix C whose elements are all non zero.

I can easily do the second part of the question. I cannot understand the logic of the second part of the question - we have proved that B=C, how can C now be non equivalent to B?

Thanks

 

[VeeEight]

Because the assumption in the first question is that A is non-singular

 

[Dick]

Given that AB = BC, and that A is non-singular, prove that B =C.

I don't know how to do matrices in these forums, so where I write a matrix, I mean (a,b,c,d)

Given that A = (3,6,1,2) and B = (1,5,0,1), find a matrix C whose elements are all non zero.

I can easily do the second part of the question. I cannot understand the logic of the second part of the question - we have proved that B=C, how can C now be non equivalent to B?

Thanks

I think you mean AB=AC. Like VeeEight said, in the first problem A is assumed to be nonsingular. The matrix you gave for A is the second part is singular. Ax=0 for some nonzero vector x. Use that to construct a C.