MATLAB: Determinant and inverse of a 3 X 3 matrix Issue

Hi I have a question:
I need to create a function that calculates the determinant and the inverse of a generic 3 X 3 matrix with the method of the cofactors and the adjoint matrix.
The function should be named invanddet3by3. The function takes a generic 3 X 3 matrix as input, and returns two outputs: the determinant and the inverse. It should do the following few things:
It calculates the determinant using the cofactors.
If the determinant is zero, the inverse is set to be an empty matrix ([])
If the determinant is non-zero, then it calculates the inverse.
However I MUST USE THE FUNCTION invanddet2by2sol provided to me which is :
function [ determinant, inverse ] = invanddet2by2sol( A )
% INVANDDET2BY2 Calculates the determinant and the inverse of a 2 X 2 matrix
determinant = A(1,1)*A(2,2)- A(1,2)* A(2,1); % calculates the determinant
if determinant ==0 % if the matrix is singular
    inverse = []; % inverse does not exist
else    
    inverse = [A(2,2)  -A(1,2); -A(2,1) A(1,1)]./determinant; % calculates the inverse
end
Here is my attempt :
function [determinant , inverse ] = invanddet3by3(A)
%INVANDDET3BY3 Calculates the determinant and the inverse of a 3 X 3 matrix by using
% cofactors and adjoint matrix
A11 = [(A(2,2) * A(3,3)) - (A(3,2) * A(2,3))]; % Cofactors 3x3 matrix A
A12 = - [(A(2,1) * A(3,3)) - (A(3,1) * A(2,3))];
A13 = [(A(2,1) * A(3,2)) - (A(3,1) * A(2,2))];
A21 = - [(A(1,2) * A(3,3)) - (A(3,2) * A(1,3))];
A22 = [(A(1,1) * A(3,3)) - (A(3,1) * A(1,3))];
A23 = - [(A(1,1) * A(3,2)) - (A(3,1) * A(1,2))];
A31 = [(A(1,2) * A(2,3)) - (A(2,2) * A(1,3))];
A32 = - [(A(1,1) * A(2,3)) - (A(2,1) * A(1,3))];
A33 = [(A(1,1) * A(2,2)) - (A(2,1) * A(1,2))];
J = [ A11 A12 A13; A21 A22 A23; A31 A32 A33]; % Adjugate Matrix
determinant = ((A(1,1) * A11) + (A(1,2) * A12) + (A(1,3) * A13)); % Determinant of A
inverse = (1/determinant) * (J'); % Inverse of A
if determinant==0
inverse=[];
end
end
My code passes all the tests for calculating the determinant and inverse correctly, but its saying: 'The submission must contain the following functions or keywords: invanddet2by2sol You MUST use the function invanddet2by2sol!'.
I have tried many things but have been unsuccessful.
Would appreciate the help,
Thanks very much.

Best Answer

In the code that you have provided, your cofactor calculations in fact consist of many 2x2 determinant calculations
    A11 = [(A(2,2) * A(3,3)) - (A(3,2) * A(2,3))]; % Cofactors 3x3 matrix A
    A12 = - [(A(2,1) * A(3,3)) - (A(3,1) * A(2,3))];
    A13 = [(A(2,1) * A(3,2)) - (A(3,1) * A(2,2))];
    etc...
You are probably intended to use invandet2by2sol to do these 2x2 determinant calculations.
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