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 :


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 

Ciara R. A Level Maths tutor, 13 plus  Maths tutor, IB Maths tutor, 1...

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