I am trying to write a method that checks if a matrix is orthogonal and return TRUE if it is or FALSE if it isn't. My problem is that my isequal() is not working how I want it to. Basically I can do the check in two ways based on the two formulas:

ONE way is check to see if the transpose of matrix R is equal to the inverse of matrix R. If they are equal then it is orthogonal. (R'=inv(R))

ANOTHER way is to check and see if matrix R times the transpose of matrix R equals the Identity matrix of R. (R'R=I) If yes then the matrix is orthogonal. I have most been using isequal() but it keeps yielding false. Can someone look at my code and tell me why this would be so?

I use Z=orth(randn(3,3)) to generate random orthogonal matrix and i call my method isortho(Z)

function R = isortho(r)
%isortho(R), which returns true if R is orthogonal matrix, otherwise returns false.
    if ismatrix(r) && size(r,1)==size(r,2) %checks if input is square matrix
       '------'
        trans=transpose(r)
        inverted=inv(r)
        isequal(trans,inverted)
        trans==inverted
        isequal(transpose(r),inv(r)) %METHOD ONE
    
        i=size(r,1);
        I=eye(i) %creating Identity matrix based on size of r
        r*transpose(r)
        r*transpose(r)==I %METHOD TWO
    
   
    
        %check if transpose of r is times inverse of r equals Identity matrix of r
        if (r*transpose(r)==I)
            R= 'True';
        else
           R= 'False';
        end
    end       
end

This is my output:

>> isortho(Z)

ans =
 ------

trans =
   -0.2579   -0.7291   -0.6339
    0.8740    0.1035   -0.4747
    0.4117   -0.6765    0.6106

inverted =
    -0.2579   -0.7291   -0.6339
     0.8740    0.1035   -0.4747
     0.4117   -0.6765    0.6106

ans =    ////isequal(trans,inverted) which yielded 0 false
     0

ans =    ////trans==inverted
     0     1     0
     1     0     0
     0     1     1

ans =      ////isequal(transpose(r),inv(r))
     0

I =
     1     0     0
     0     1     0
     0     0     1

ans =
    1.0000         0    0.0000
         0    1.0000    0.0000
    0.0000    0.0000    1.0000

ans =
     1     1     0
     1     1     0
     0     0     1

ans =
False
>> 

Could someone help me fix this or tell my why the isequal() is failing when matrix inverted and trans appear to be the same?