Last Updated: 27 Nov, 2020

Matrix Game

Easy

Asked in companies

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Problem statement

Ninja is a teacher at a school. He introduced a game of matrix. He gives a square matrix, i.e., NxN matrix, to all the school students and asks them to check if the matrix is idempotent or not.

A matrix is an idempotent matrix if a matrix multiplied by itself returns the same matrix. The matrix M is said to be an idempotent matrix if and only if M * M = M. In the idempotent matrix, M is a square matrix.

Among them, a student Ninja is new to programming; he doesn’t have much experience; he asks you to solve the problem. Can you help Ninja figure out whether the matrix is idempotent?

Input Format:

The first line of input contains an integer ‘T,’ denoting the number of test cases. The test cases follow.

The first line of each test case contains a number ‘N’ denoting the number of rows and columns of the matrix.

The next ‘N’ lines of each test case contain ‘N’ integers in each line.

Output Format:

For each test case, if Ninja managed to solve the problem, print “True”. Otherwise, print “False”.

Print the output of each test case in a separate line.

Note:

You are not required to print the expected output; it has already been taken care of. Just implement the function.

Constraints:

1<= T <= 50
1<= N <= 100 

 Time Limit: 1 sec

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Approaches

01 Approach

The idea is to maintain a 2D array that will store the result of the multiplication of a given matrix.

The steps are as follows:

We will maintain an integer 2D array of size NxN initially empty, which will store the result of multiplication of a given matrix with itself.
We will initialize the resultant 2D array with 0.
We will iterate from i = 0 to i = N - 1:
- For each row in the given matrix, we will perform the following operations:
- We will iterate through from j=0 to j=N since we need to multiply the matrix by itself.
  - We will iterate through from k=0 to k=N and multiply the matrix by itself, storing the result of multiplication in the resultant 2D array.
After all the iteration is done, the resulting 2D array will multiply the given matrix by itself.
Now, we will check if the given resultant matrix matches the given matrix. If it does, then return true. Otherwise, return false.

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