We know that,

The number of rows and columns that a matrix has is called its order or its dimension. By convention, rows are listed first; and columns second.

Also,

Addition or subtraction of matrices is possible only if the matrices are of same order.

That is,

If A and B are two matrices and if they are needed to be added, then if order of A is m × n, order of B must be m × n.

We have matrices A and B, where

We know what order of matrix is,

If a matrix has M rows and N columns, the order of matrix is M × N.

In matrix A:

Number of rows = 2

⇒ M = 2

Number of column = 2

⇒ N = 2

Then, order of matrix A = M × N

⇒ Order of matrix A = 2 × 2

In matrix B:

Number of rows = 2

⇒ M = 2

Number of columns = 3

⇒ M = 3

Then, order of matrix B = M × N

⇒ order of matrix B = 2 × 3

Since,

Order of matrix A ≠ Order of matrix B

⇒ Matrices A and B cannot be added.

Thus, matrix A and matrix B cannot be added.