# Finding Inverse of a Non-Square Matrix

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#### rajez79

##### Newbie level 4
Hi All,

While doing a DePrecoder for LTE_MIMO, i need to do matrix division. Since matrix division is not possible, i tried to take the inverse of the matrix and multiply it. If it is a square matrix then the above condition will work fine. how to do that for a Non_Square Matrix....??

Ex...,

a = [1 2 3; 4 5 6];
b = [4 5; 2 3; 5 6];

c = a * b;

Now if i want to find matrix b means....

b = c * (1/a) = c * inv(a);

Here inv(c) will not work coz it is not a square matrix. Please help me in finding it.

NOTE : PseudoInverse - pinv() in MATLAB is also not working.

#### puripong

##### Member level 2
From the matrix equation

c = a * b ; where a is non-square-matrix

You want to find matrix b, I think we must multiply this eq. with the transpose of matrix a

at*c = (at*a)*b ; where at is the traspose matrix of a

Now at*a is square matrix

b = inv((at*a)) * at*c

#### puripong

##### Member level 2
You mean at*a is not invertible ?

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