If A,B are two matrices such that A*B and A+B are both defined then A,B are of__________order? Pls solve this problem with explaination.

For addition of two matrices, it is required that the matrices should be of the same order.

For multiplication of two matrices A of order m×n and B of order p×q, it is required that

n = p … (1)

For addition to be possible,

m = p … (2)

n = q … (3)

From (1) and (3), we get

p = q … (4)

From (1) and (2), we get

n = m … (5)

From (4) and (5), we can conclude that A and B are square matrices and their orders are one and the same.

Thus, for both addition and multiplication of two matrices to be possible, it is required that both the matrices should be of same order and they should be square matrices.