Question

if A and B are two matrices such that A+B and AB are both defined, then A and B are?
A) both identity matrices
B) both null matrices
C) both matrices of same order
D) both square matrices of same order

Answer 1

hère, i m not only answering but explaining it
hope it helps u..

For addition of two matrices, it is required that the matrices should be of the same order.

For multiplication of two matrices A of order m×n and B of order p×q, it is required that

n = p … (1)

For addition to be possible,

m = p … (2)

n = q … (3)

From (1) and (3), we get

p = q … (4)

From (1) and (2), we get

n = m … (5)

From (4) and (5), we can conclude that A and B are square matrices and their orders are one and the same.

Thus, for both addition and multiplication of two matrices to be possible, it is required that both the matrices should be of same order and they should be square matrices.

Let's discuss it practically.

For example, the matrices A4×4andB4×4 are compatible for both the operations.

Also, if we take two matrices, A4×3andB3×4, multiplication is possible but addition is not possible.

Also, if we take two matrices, A4×3andB4×3, addition is possible but multiplication is not possible.

990 Views ·
If there are two matrices A and B and A+B = AB, then how do we prove that AB = BA?

How can we find out if A and B are two square matrices such that B=-A^-1BA then (A+B)^2=()?

IF A and B are two matrices than what is the value of A.*B?

What if A and B are nonzero square matrices such that AB=0?

What does [A,B] represent if A and B are matrices?

Matrices can be added or multiplied only if the order of the matrices are same.Here you say that A and B are two matrices and A+B and AB are defined.That means that the number of rows and number of columns are same for both the matrices.

Note:-

A matrices of order 2x3 (where 2 is the number of rows and 3 is the number of columns) does not have the same order of a matrices whose order is 3x2(where 3 is the number of rows and 2 is the number of columns).

I hope this answers your question.



mark me as brainliest and fllw me for further queries

Answer 2

hère, i m not only answering but explaining it

hope it helps u..

For addition of two matrices, it is required that the matrices should be of the same order.

For multiplication of two matrices A of order m×n and B of order p×q, it is required that

n = p … (1)

For addition to be possible,

m = p … (2)

n = q … (3)

From (1) and (3), we get

p = q … (4)

From (1) and (2), we get

n = m … (5)

From (4) and (5), we can conclude that A and B are square matrices and their orders are one and the same.

Thus, for both addition and multiplication of two matrices to be possible, it is required that both the matrices should be of same order and they should be square matrices.

Let's discuss it practically.

For example, the matrices A4×4andB4×4 are compatible for both the operations.

Also, if we take two matrices, A4×3andB3×4, multiplication is possible but addition is not possible.

Also, if we take two matrices, A4×3andB4×3, addition is possible but multiplication is not possible.

990 Views ·

If there are two matrices A and B and A+B = AB, then how do we prove that AB = BA?

How can we find out if A and B are two square matrices such that B=-A^-1BA then (A+B)^2=()?

IF A and B are two matrices than what is the value of A.*B?

What if A and B are nonzero square matrices such that AB=0?

What does [A,B] represent if A and B are matrices?

Matrices can be added or multiplied only if the order of the matrices are same.Here you say that A and B are two matrices and A+B and AB are defined.That means that the number of rows and number of columns are same for both the matrices.

Note:-

A matrices of order 2x3 (where 2 is the number of rows and 3 is the number of columns) does not have the same order of a matrices whose order is 3x2(where 3 is the number of rows and 2 is the number of columns).

I hope this answers your question.

mark me as brainliest and fllw me for further queries