Question

A is of order $m \times n$ and B is order of $p \times q$, addition of A and B is possible only when
A) m=p
B) n=q
C) n=p
D) m=p, n=q

Answer 1

Hint : In mathematics, a matrix is a rectangular array of numbers, expressions or symbols, arranged in a row and columns. Horizontal rows are denoted by ‘m’ whereas the Vertical columns are denoted by ‘n’. Thus a matrix (m×n) has m and n numbers of rows and columns respectively.
The addition of two matrices can be done by addition of corresponding terms in the matrix.
There are basically two criteria which define the addition of matrix which are:

Two matrices can be added if the order of the matrices is equal, i.e. the two matrices must have the same number of rows and columns.
The addition of matrices is not defined for matrices of different sizes.

Complete step by step solution : According to the question,
The order of A = m×n
The number of rows in A = m
The number of columns in A = n
The order of B = p×q
The number of rows in B = p
The number of columns in B = q
Addition of A and B is possible only when both the matrices have the same number of rows and columns.
So, when m=p and n=q then only addition of A and B is possible.

Hence option ‘D’ is the correct answer.

Note : For addition/subtraction, each element of the first matrix is added/subtracted to the elements present in the second matrix. When we change the sign of every element of matrix A, then it will become the additive inverse of the matrix A. The sum of matrix A and its additive inverse is always zero.