Definition:  A matrix is a rectangular array of numbers.  The numbers in the array are called entries in the matrix.  A matrix A with n rows and n columns is called a square matrix of order n, and the entries a11, a22, a33,...,ann are on the main diagonal of A.

Two matrices are considered equal if they have the same size and the corresponding entries in the two matrices are equal.

Example 1:

Consider the matrices

Here X does not equal Z since X and Z do not have the same size.  For the same reason, Y does not equal Z.  Also, X does not equal Y since not all the corresponding entries are equal.