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Multiplying Matrices

Updated on November 1, 2011

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 )


( 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 )




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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    • t.elia profile image

      t.elia 4 years ago from Northern Ireland

    • Caleb DRC profile image

      Caleb DRC 5 years ago

      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.

    • profile image

      having difficulty 6 years ago

      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?

    • t.elia profile image

      t.elia 7 years ago from Northern Ireland

      Hi Irish,

      I don't believe it for a

      Thanks for dropping by.

    • theirishobserver. profile image

      theirishobserver. 7 years ago from Ireland

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

    • t.elia profile image

      t.elia 7 years ago from Northern Ireland

      Thanks Apostle Jack.Nice of you to drop in and look around.

    • Apostle Jack profile image

      Apostle Jack 7 years ago from Atlanta Ga

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