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# Linear Algebra: Should I multiply these two translation matrices together?

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If I have 2 translation matrices.

Matrix A: Translates 2 units up the Y axis.

Matrix B: Translates 3 units up the Y axis, and 2 units up the X axis.

If I multiple these two matrices together, will the resulting matrix translate 5 units up the Y axis, and 2 units up the X axis?

That is my goal, and apparently I'm just enough years beyond Linear algebra to remember.

Thanks!
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Commented:
Yes , Exactly ..
if you have a 3D vector for translating and rotating you must add one row to your matrix i will show you :

| X |
V = | Y |
| Z |
| 1 |

Translatin Matrix for translating a,b,c is :

Trans = | 1 0 0 a |
| 0 1 0 b |
| 0 0 1 c |
| 0 0 0 1 |

now if you Multiple your Vector to Trans Matrix the Result Matrix is  :

New V = | X+a  |
| Y+b  |
| Z+c  |
| 1      |

Now you Can Remove the added Row ..

and for Trans 2 o 3 o more time you just need to translate the result again and again ..

Commented:
Thanks for the tips!
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