## What are the properties of adjoint of a matrix?

## How to find the adjoint of a scalar multiplication?

- The
**adjoint**of a scalar multiplication is equal to the product of the scalar raised to n-1 and the**adjoint**of the**matrix**, where n is the order of the**matrix**. Let A be a square**matrix**of order n, if the rank of**matrix**A is less than or equal to n-2, then the**adjoint**of**matrix**A results in 0.

## What is an adjugate matrix?

- Adjugate
**matrix**is another term used to refer to the**adjoint matrix**in linear algebra. An adjugate**matrix**is especially useful in applications where an inverse**matrix**cannot be used directly. The**adjoint**of a**matrix**is obtained by taking the transpose of the cofactor elements of the given**matrix**.

## How to find the determinant of adjoints?

- determinant of
**adjoint**A is equal to determinant of A power n-1 where A is invertible n x n square**matrix**. You can also take examples to verify these**properties**.

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