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?
Question
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?
Solution
Sure, I can help Ninja figure out whether the matrix is idempotent or not. Here are the steps to solve this problem:
Step 1: First, we need to understand the size of the matrix. Since it's a square matrix, it means the number of rows is equal to the number of columns. Let's denote this number as N.
Step 2: Next, we need to multiply the matrix by itself. This is done by taking each element in the first row of the first matrix and multiplying it by each element in the first column of the second matrix, then adding the results to get the first element of the resulting matrix. This process is repeated for all rows and columns.
Step 3: After we have the resulting matrix, we need to compare it with the original matrix. If every corresponding element in the two matrices is equal, then the matrix is idempotent. If there's at least one pair of elements that are not equal, then the matrix is not idempotent.
Step 4: Return the result. If the matrix is idempotent, return true or yes. If the matrix is not idempotent, return false or no.
This is a basic algorithm to check if a matrix is idempotent. Depending on the programming language Ninja is using, the implementation might be slightly different, but the logic remains the same.
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