Question

If A = (a;))mxn and B = (bij)pxq and AB=BA, then
n=p
On=p, m=q
m=n=p=q
m=q​

Answer 1

Answer:

A op= mo

B qo= pq

Step-by-step explanation:

because if we divide ➗

on= p, m= q

by

m=n = p = q

op = pq

so the answer is

mo pq

Answer 2

Question: If A = $(a_{ij})_{m\times n}$, B = $(b_{ij})_{p\times q}$ and AB = BA, then

n = p, m = q, m = n = p = q and m = q.

Answer:

The correct answer is n = p and q = m.

Step-by-step explanation:

It is given that A = $(a_{ij})_{m\times n}$, B = $(b_{ij})_{p\times q}$ and AB = BA.

Since A = $(a_{ij})_{m\times n}$.

⇒ A is a matrix of (m × n) order.

⇒ A has m number of rows and n number of columns.

Similarly,

We have, B = $(b_{ij})_{p\times q}$.

⇒ B is a matrix of (p × q) order.

⇒ B has p number of rows and q number of columns.

Then,

The multiplication of A and B, i.e., AB is possible when n = p.

And the matrix AB obtained is of order m × q.

In the same manner,

The multiplication of B and A, i.e., BA is possible when q = m.

And the matrix BA obtained is of order p × n.

Therefore, the required answer is n = p and q = m.

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