Question

# Find the order of B matrix if A is a $3 \times 4$ matrix and B is a matrix such that A’B and BA’ are both defined.:$(a){\text{ 3}} \times {\text{4}}$(b){\text{ 3}} \times 3$(c){\text{ 4}} \times {\text{4}}$$(d){\text{ 4}} \times 3$

Hint: In the above given question, we are asked to find out the order of the matrix for which various conditions are already provided. By using these conditions one by one, first of all find out the number of rows in the matrix and then using the other conditions, find out the number of columns in the given matrix.

We are given in the question that, A is a $3 \times 4$ matrix, therefore we know that,
Order of A’ will be ${\text{4}} \times 3$.
Since, it is given that A’B exists and we already know that A’ is a ${\text{4}} \times 3$ matrix.
Now, we know that B has 3 rows and 4 columns, so we can say that B is a $3 \times 4$ matrix.
Hence, the required solution is the option $(a){\text{ 3}} \times {\text{4}}$.