Idempotent Matrix Verification

Determine if a given N * N matrix is an idempotent matrix. A matrix is considered idempotent if it satisfies the following condition:

M * M = M

Input:

The first line contains a single integer N, denoting the size of the matrix. The next N lines each contain N space-separated integers, representing the elements of the matrix.

Output:

Output 'true' if the matrix is idempotent; otherwise, output 'false'.

Example:

Input:
2
1 0
0 1
Output:
true

Constraints:

  • 1 <= N <= 103
Note
This task only requires determining the property of the matrix without additional output formatting.
AnswerBot
1d

Check if a given matrix is idempotent by verifying if M * M equals M.

  • Calculate the product of the matrix with itself and compare it with the original matrix.

  • If the product equals the original matrix, ...read more

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