# Idempotent Matrix Calculator Online

### Explanation:

A matrix is said to be idempotent if it's square is equal to orignal matrix. A2 = A
or
A square matrix known as an idempotent matrix produces the same matrix when multiplied by itself. In the event where M2 = M, a matrix M is called as idempotent matrix. Additionally, every identity matrix is an idempotent matrix.

### What is An Idempotent Matrix?

A square matrix that is idempotent multiplies back into itself to produce the original square matrix. When a matrix M is multiplied by itself, M2 = M, it returns the same matrix M.

### Properties of Idempotent Matrix

A matrix that is idempotent has the following significant characteristics.

• An idempotent matrix is a matrix which must be a square matrix.
• There are equal numbers of rows and columns in the idempotent matrix.
• An idempotent matrix is a matrix which is also a singular matrix.
• The items outside of the diagonal can be non zero elements.
• An idempotent matrix has eigenvalues that are either 0 or 1.
• A matrix's rank is equal to its trace when it is an idempotent matrix.
• An idempotent matrix's trace is always an integer.

#### How to use check Idempotent Matrix Calculator?

• Firstly, you need to enter the dimension of the matrix. Enter number of rows in "Rows" input field and Enter number of columns in "Columns" input field.
• Then press the button "Set Matrix".
• An empty matrix will appear below and then you can enter your values inside the matrix.
• After entering all the values press "Solve" button, the result will automatically appear below which check whether the matrix is Idempotent matrix or not.

Idempotent Matrix Example Image:

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