Chapter 1 Section 1.6 Algebraic Properties of Matrix Operations

In general matrices do not commute, but one power of a matrix A will always commute with another power of A.

Identity Matrices A matrix with the same number of rows and columns is called square. A square matrix with 1's down the top left to bottom right diagonal and 0's off that diagonal is called the identity matrix. They come in different size identity matrices. 2  2 3  3 4  4 An identity matrix has the property that if you multiply it either on the right or left by any conformable matrix you get the conformable matrix (i.e. I n A = A and AI n = A ). The matrix I n for matrices acts like the number 1 for numbers.