Question

If two matrices A and B are of order \[p \times q\] and \[r \times s\] respectively, can be subtracted only if,
A. \[p = q\]
B. \[p = q,r = s\]
C. \[p = r,q = s\]
D. None of these

Answer 1

Hint: A matrix (\[p \times q\]) has p and q numbers of rows and columns respectively. Two matrices can be subtracted only if the order of the matrices is equal, i.e., the two matrices must have the same number of rows and columns. The subtraction of matrices is not defined for matrices of different sizes.

Complete step by step Solution:
The order of matrix A = \[p \times q\]
The number of rows in matrix A = p
The number of columns in matrix A = q
The order of matrix B = \[r \times s\]
The number of rows in matrix B = r
The number of columns in matrix B = s
Subtraction of matrices A and B is possible only when both matrices have the same number of rows and columns.
So, when p=r and q=s only then subtraction of A and B is possible.

Therefore, the correct option is (C).

Note:For addition/subtraction, each matrix element of the first matrix is added/subtracted to the matrix elements present in the second matrix. Addition/Subtraction of two matrices is possible only when both the matrices have the same number of rows and columns.