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In linear algebra, a matrix is said to be symmetric, if the square matrix is equal to its transpose. The symmetric matrix is only possible to check if it is a square matrix. Otherwise, the number of rows and columns in the original matrix will differ from the number of rows and columns in the transpose matrix.

The transpose of a matrix can be defined as a new matrix whose rows are the columns of the original matrix and the columns are the rows of the original matrix. If A is a matrix then it's transpose is denoted as ${\mathrm{A}}^{\mathrm{T}}$.

EXAMPLE OF THE SYMMETRIC MATRIX:

Let the matrix be: 

Now the transpose matrix will be:

Now, if we compare each element of matrix A with each element of matrix AT index wise, we will get that A = ${\mathrm{A}}^{\mathrm{T}}$

Therefore, matrix A is said to be a symmetric matrix.

INPUT: A matrix A
OUTPUT: whether it is symmetric or not

PROCESS:
Step 1: [Taking the inputs]
	Read m, n [The number of rows and columns of the matrix]
Step 2: [Checking for a symmetric matrix]
		If m=n then
		[taking the elements of the matrix]
		For i=0 to m-1 repeat
			For j=0 to n-1 repeat
				Read a[i][j]
			[End of ‘for’ loop]
		[End of ‘for’ loop]
		[finding the transpose of a matrix]
	 	for i = 0 to m-1 repeat
        			for j = 0 to n-1 repeat
        				Set t[j][i]<-a[i][j]
			[End of ‘for’ loop]
		[End of ‘for’ loop]
		[printing the transpose matrix]
		Print "The transpose of the matrix is:"
		For i=0 to n-1 repeat
			For j=0 to m-1 repeat
				Print t[i][j]
				If j=m-1 then
					Move to the next line
				[End of ‘if’]
			[End of ‘for’ loop]
		[End of ‘for’ loop]
		[checking if the matrix is symmetric]
		For i= 0 to m-1 repeat 
        			For j= 0 to n-1 repeat
            				If a[i][j] ≠ t[i][j] then
                				Print "The Matrix is not Symmetric"
                				exit 
				[End of ‘if’]
        			[End of ‘for’ loop]
    		[End of ‘for’ loop]
    		Print "The matrix is symmetric”
	else
		print "The matrix is not a square matrix"
[End of ‘if’]

Step 3: Stop.