Equality of Matrices

Two matrices are equal if all three of the following conditions are met:

•  Each matrix has the same number of rows.
•  Each matrix has the same number of columns.
•  Corresponding elements within each matrix are equal.

Consider the three matrices shown below.


If A = B then we know that x = 34 and y = 54, since corresponding elements of equal matrices are also equal.
We know that matrix C is not equal to A or B, because C has more columns.

•  Two equal matrices are exactly the same.
•  If rows are changed into columns and columns into rows, we get a transpose matrix. If the original matrix is A, its transpose is usually denoted by A^' or A^t.
•  If two matrices are of the same order (no condition on elements) they are said to be comparable.
• If the given matrix A is of the order m x n, then its transpose will be of the order n x m. 

1. Column matrix - a matrix that has only one column.
2. Row matrix - a matrix that has only one row.