Question

If A is a matrix of order (p×q) and B is a matrix such that AB=BA then order of B=​

Answer 1

Answer:

The order B is p × q.

Step-by-step explanation:

Given :

→ Order of matrix A = p × q

→ AB = BA

We know that two matrices can be multiplied only when :

→ No. of rows in A = No. of columns in B

We know that, after multiplying, the order of the product will be :

→ No. of columns in A × No. of rows in B

So, in accordance with the given condition, i.e., AB = BA, we can say that :

→ A, B are square matrices with p = q

Therefore, they will be having the same order.

→ Order of matrix A = Order of matrix B

→ p × q = Order of matrix B