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.

Note:

·  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 At.

·  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.

Example 1: The notation below describes two matrices A and B.

where  i= 1, 2, 3 and j = 1, 2

Solution:

The correct answer is (E)

Matrix A has 3 rows and 2 columns; that is, 3 rows each with 2 elements. This adds up to 6 elements not 5.

The dimension of matrix B is 2×4 and not 4×2, which means that matrix B has 2 rows and 4 columns and not 4 rows and 2 columns.

Element B21 refers to the first element in the second row of matrix B, which is equal to 555 but not 222.

Matrix A and B cannot be equal because, we don’t know anything about the entries of matrix A. They are just unknown for us. Moreover, their orders are also different.