# Multiplying Matrices

**What is a Matrix?**

**A matrix is defined as an ordered rectangular array of numbers. They can be used to represent systems of linear equations. They are a key tool in linear Algebra.**

**This ordered array basically describes the size of a Matrix. **

**The order is the number of Rows x number of Columns**

**so a 3 x 4 Matrix has **

**3 Rows and**

**4 Columns**

**In order to multiply two Matrices they have to be compatible.**

**The Rule:-**

**When multiplying two Matrices; **

**if the first Matrix has order (a x b) **

**and the second Matrix has order (c x d)**

**( a x b ) ( c x d )**

**b must equal c or the two Matrices can't be multiplied**

**If they are compatible then the answer will be a Matrix which has the order ( a x d )**

**Example **

** ( 3 x 4 ) ( 4 x 3 )**

** = ( 3 x 3 ) Matrix**

**See worked example below**

## Summarisation of worked Example

**In the above worked example**

**we had a ( 2 x 3 ) Matrix which was the first one having order ( a x b )**

**and**

**then a ( 3 x 4 ) Matrix which was the second one having order ( c x d )**

**( a x b ) ( c x d )**

**( 2 x 3 ) ( 3 x 4 )**

**As seen above b = c**

**The answer is a Matrix which has the order ( a x d )**

** ( 2 x 4 )**

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## Comments 7 comments

It's beyond me...but i admire others who have the education.

now that is complicated....I like basic maths...very handy when I was landscaping....but this is beyond me.....Irish

i can see what you're talking about here but when the question is 'the answer to this is of order a x b find a and b' how do you go about doing it?

I have linked my readers to this hub several times. You have done a superb and very professional job in explaining how to multiply matrices.

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