Identity matrix

Definition

An identity matrix is a square matrix with ones on the diagonal and zeros elsewhere. It acts as the multiplicative identity in matrix multiplication.

5 Must Know Facts For Your Next Test

1. Multiplying any matrix by its corresponding identity matrix leaves the original matrix unchanged.
2. The identity matrix for a 2x2 system is $\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$.
3. In solving systems of equations, using the identity matrix can help find the inverse of a given matrix.
4. An identity matrix is always square, meaning it has an equal number of rows and columns.
5. The determinant of an identity matrix is always 1.

Review Questions

• What happens when you multiply any square matrix by its corresponding identity matrix?
• Write down the identity matrix for a 3x3 system.
• Why is the concept of an identity matrix important in finding inverses of matrices?

Related terms

Inverse Matrix: A matrix that, when multiplied by its original matrix, yields the identity matrix.

Determinant: A scalar value that can be computed from the elements of a square matrix and encodes certain properties of the transformation described by the matrix.

Matrix Multiplication: An operation that takes two matrices and produces another matrix, where each element is derived from multiplying elements from rows and columns of the input matrices.