Matrix is symmetric
You are given a square matrix, return true if the matrix is symmetric otherwise return false.

A symmetric matrix is that matrix whose transpose is equal to the matrix itself.

Example of symmetric matrix :

Input Format:

The first line contains an Integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow. The first line of each test case contains the size of the square matrix 'N'. The second line of each test case contains the 'N' * 'N' Integers separated by a single space (the matrix is entered row-wise)

Output format :

For each test case/query, print whether the given matrix is symmetric or not. Output for every test case will be printed in a separate line.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1

Question

Matrix is symmetric

You are given a square matrix, return true if the matrix is symmetric otherwise return false.

A symmetric matrix is that matrix whose transpose is equal to the matrix itself.

Example of symmetric matrix :

Symmetric Example

Input Format:

The first line contains an Integer 'T' which denotes the number of test cases or queries to be run. Then the test cases follow.

The first line of each test case contains the size of the square matrix 'N'.

The second line of each test case contains the 'N' * 'N' Integers separated by a single space (the matrix is entered row-wise)

Output format :

For each test case/query, print whether the given matrix is symmetric or not.

Output for every test case will be printed in a separate line.

Note:

You do not need to print anything, it has already been taken care of. Just implement the given function.

Constraints:

1 <= T <= 10
1 <= N  <= 10^2
-10^9 <= data <= 10^9

Where 'data' denotes the element in the given 'matrix'.

Time Limit: 1 sec

Accepted Answer

A Simple solution is to do the following.
1) Create transpose of given matrix.
2) Check if transpose and given matrices are same or not.

Accepted Answer

Brute Force

Create another matrix ‘TRANSPOSE’ of the same size initially having all zeros.
Now replace ‘TRANSPOSE’ (i,j) with ‘MATRIX’ (j,i).
And now traverse both matrixes element by element if anywhere there is inequality return false, else continue.
In the end, return true as you traverse.

Space Complexity: O(1)Explanation:

O(N ^ 2), Where ‘N’ is the size of the square matrix.

Since an extra matrix of size ‘N’ * ‘N’ is created while making transpose of the matrix. Hence overall space complexity is O(N * N).

Time Complexity: O(n^2)Explanation:

O(N^2) , Where ‘N’ is the size of the square matrix.

Since every element is visited once and there are ‘N’ ^2 elements in total. Hence the overall time complexity is O(N^2).

Accepted Answer

Optimised Approach

Traverse the matrix element by element and compare ‘MATRIX' ( I, j) with 'MATRIX" ( j, i).
And if anywhere there inequality exists between them simply return false from that point else continue.
In the end, if not returned previously from anywhere else just return true, as ‘MATRIX’ is symmetric.