Identity matrix: concept and properties

THE identity matrix or drive matrix, indicated by the letter I, is a type of square and diagonal matrix.

This is because all the elements on the main diagonal are equal to 1 and the others equal to 0.

Remember that a square matrix is ​​one that has the same number of columns and rows.

Example:

Be THE an identity matrix of order n, THE is the identity matrix of order n (I_no).

properties

• The identity matrix is ​​indicated by I_no, where the no matches the order of the array. So if it has three rows and three columns it is called an identity matrix of order 3.
• THE. I_no = I_no. A = A: This property involves matrix multiplication, where A is square of order n. This means that the identity matrix is ​​neutral, that is, any matrix multiplied by the identity matrix will result in the matrix itself.

Fell in the Entrance Exam!

(UFU-MG) Let A, B and C be square matrices of order 2, such as A. B = I, where l is the identity matrix.

The matrix X such that A. X. A = C is equal to:

a) B. Ç. B
b) (A²) ^-1. Ç
c) C. (THE^-1)²
gives. Ç. B

See Answer

Alternative a: B. Ç. B

Read too:

• Matrices
• Matrices - Exercises
• Types of Matrices
• Inverse matrix
• Matrix Multiplication
• Matrices and Determinants