Proving the orthogonality of Square Matrix and its Transpose

Question

I've a square matrix, that has an equal number of rows and columns. So how should I prove its orthogonality? Been searching around, but couldn't find something that could be helpful.

Here's a given DCT-matrix, which I've to find the orthogonality of:

    mat = [0.5000   0.5000   0.5000   0.5000   
    0.6533   0.2706  -0.2706  -0.6533
    0.5000  -0.5000  -0.5000   0.5000  
    0.2706  -0.6533   0.6533  -0.2706];

Which I did. The square matrix and its transpose is given below with following commands.

>> mat*mat' %%Transpose
>> mat'*mat %%Square

ans =

    1.0000         0         0         0
         0    1.0001         0         0
         0         0    1.0000         0
         0         0         0    1.0001


ans =

    1.0000    0.0000   -0.0000   -0.0000
    0.0000    1.0000   -0.0000   -0.0000
   -0.0000   -0.0000    1.0000    0.0000
   -0.0000   -0.0000    0.0000    1.0000

As I understand by reading from this site: Click Here It says "when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix."

If you ask me, then I can actually see the orthogonality, since it's mostly identity diagonal, the thing is will the +0.0001 make a difference, since two of the numbers are 1.0001 and the others are 1.0000? it is stated that it is orthogonal in the task description, just want to be sure.

My question is: Is the matrix orthogonal?