Question

If A and B are matrices,then which from the following is true ?
a. A+B is not equal to B+A
b. (At)t is not equal to A
c. AB BA.
d. all are true
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Answer 1

The form which is true is AB≠BA.

Given:

First matrice = A

Second matrice = B

To Find:

Which of the given statements is true among the given options

Solution:

The given options belong to the property of matrices. Looking at the given options as per matrices property -

As per the associative property of matrices,

A+B = B+A  

Thus, option a is incorrect

As per the transpose property of matrices

(A^t)^t = A

Thus, option b is incorrect

Now, since options a and b are incorrect, thus option d stating all are true becomes automatically incorrect.

However, When two matrices are multiplied,

Then, AB ≠BA

Answer: The correct statement is AB ≠BA

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Answer 2

The true form is AB≠BA.

Given: First Matrice = A, Second Matrice = B

TO FIND: Which option of the following assertions is true?

SOLUTION:

The available options fall under the category of matrices. Examining the available options in light of the matrices' properties

According to matrices' associative properties,

A+B = B+A

Option A is therefore untrue.

According to the matrices' transpose property

(A^t)^t = A

Option b is therefore untrue.

Option d, which states that all are true, is now inevitably erroneous because options a and b are incorrect.

But when two matrices are combined,

Next, AB ≠BA

The true form is AB≠BA.

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