# How do I multiply 2 matrices?

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To multiply two matrices we need to name them A and B.

If for example we have 2 2X2 square matrices we know this will create a 3rd 2x2 martix

For this example we will use :

A:

2 -1

3 4

and B:

5 0

-2 -2

To multiply these we complete this table:

(1st row of A X 1st column B) |  (1st row A X 2nd column B)

---------------------------------------------------------------------------------------

(2nd row A X 1st column B )| (2nd row A X 2nd     column B)

this therefore gives us :

(2X5)+(-1X-2) | (2X0)+(-1X-3)

-------------------------------------------

(3X5)+(4X2) |  (3X0)+(4X-3)

resulting in the matrix AB=

12  3

7  -12

if you have trouble with this its easy to remmeber, multiply the rows by the columns

by doing this you can tell what order a matrix will come out as for example

a 2X2 matrix multiplied by a 2X1 matrix will give a 2X1 matrix as you are multiplying the rows of the first by the columns of the second.

Hope this helped, feel free to ask any questions for futher clarification

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