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

Question

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.

Accepted Answer

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, then it is idempotent.
If the product does not equal the original matrix, then it is not idempotent.

Idempotent Matrix Verification

Input:

Output:

Example:

Input:

Output:

Constraints:

Note

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