College Algebra (6th Edition)

A matrix is a set of numbers, arranged into rows and columns, placed in brackets. The numbers inside the brackets are called elements of the matrix. A matrix of order $m\times n$ has $m$ rows and $n$ columns. To add or subtract two matrices, they must have the same order. Otherwise, the sum/difference is not defined. Matrices of the same order are added or subtracted by adding or subtracting corresponding elements. Example: $A= \left[\begin{array}{ll} 1 & 2\\ 3 & 4\\ 5 & 6 \end{array}\right]$ is a 3$\times$2 matrix, while $B=\left[\begin{array}{lll} 1 & 2 & 3\\ 4 & 5 & 6 \end{array}\right]$ is a 2$\times$3 matrix so the sum $A+B$ and the difference $A-B$ are not defined.