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.
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we know that
If a ordered pair (x,y) is a solution of the equation, then the ordered pair must satisfy the equation
we have the equation
Let's verify all the cases to determine the solution to the problem.
<u>case A)</u> point 
Substitute the values of x and y in the equation
-------> is true
therefore
The point is a solution of the equation
<u>case B)</u> point 
Substitute the values of x and y in the equation
-------> is true
therefore
The point is a solution of the equation
<u>case C)</u> point 
Substitute the values of x and y in the equation
-------> is not true
therefore
The point is not a solution of the equation
<u>case D)</u> point 
Substitute the values of x and y in the equation
-------> is not true
therefore
The point is not a solution of the equation
therefore
<u>the answer is </u>
