Answer with Step-by-step explanation:
We are given that
A and B are matrix.
A.We know that for two square matrix A and B
Then, 
Therefore, it is true.
B. det A is the product of diagonal entries in A.
It is not true for all matrix.It is true for upper triangular matrix.
Hence, it is false.
C.

When is a factor of the characteristics polynomial of A then -5 is an eigenvalue of A not 5.
Hence, it is false.
D.An elementary row operation on A does not change the determinant.
It is true because when an elementary operation applied then the value of matrix A does not change.
Answer:D
Step-by-step explanation:
Let's set it up like this:

Multiply both sides by



We are then going to use the distributive property. Since we also know that the opposite of an number that is squared is the square root, we can also apply that. We would be left with something like this:

The variable

can be both positive or negative.
We have found successfully our answer.
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish<span />