# How to multiply a 3*3 matrix ?

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

I assume you mean how to multiply a 3x3 matrix with another 3x3 matrix.

Lets use the two matrices:

A =    (a1  a12  a13; a21  a22  a23; a31  a32  a33)

i.e., the rows are (a11  a12  a13); (a21  a22  a23) and (a31  a32  a33)

&

B = (b11  b12  b13; b21  b22  b23; b31  b32  b33)

where the rows are (b11  b12  b13); (b21   b22   b23) and (b31  b32  b33)

The resultant matrix of product of these two 3x3 matrices will also be a 3x3 matrix, X with rows (x11  x12  x13); (x21  x22  x23) and (x31  x32  x33)

Here x11 = a11xb11  + a12xb21 + a13xb31;

x12 = a11xb12 + a12xb22 + a13xb32.........and so on

x33 = a31xb13 + a32xb23 + a33xb33.

that is how one can calculate the product of a 3x3 matrix with another 3x3 matrix.

catherine123 | eNotes Newbie

Posted on

Take the resultanta matrix as

res11 res12 res13

res21 res22 res23

res31 res32 res33

Multiplying each element of first row of 1st matrix and 1st col of 2nd matrix gives res11 value.

Follow the same for all other cell values.

Use Matrix Multiplication Tutorial at easycalculation site for more detailed explanation

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