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 = M.

Iterate through the matrix and multiply it with itself to check if it equals the original matrix.
If the condition M * M = M is satisfied, then the matrix is idempotent.
If the condition is not satisfied, then the matrix is not idempotent.

Idempotent Matrix Verification

Input:

Output:

Example:

Input:

Output:

Constraints:

Note

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