Warlock noticed that Nathan had already finished and couldn’t keep his amazed face from showing at the back. The other student couldn’t tell since their eyes were glued to Selene; it was obvious that she was having some trouble with the math questions.

A few minutes passed before Selene was able to finish answering. Nathan timed himself up so it would appear that he finished the same time as Selene.

Nathan was a good actor, only three people were able to figure out his intention because they had their eyes on him from the beginning.

“It seems that you had fun with that little problem, here comes the next one,” Professor Damian said with a smile.

The students felt hate and wanted to cry as they heard the professor’s words, was it a little problem? We are not a top-class university, how high is your expectation?

The professor continued, disregarding the eyes of the students that wanted to melt him with their stares.

“This would be the final test, but if one of you is able to answer this then another bonus question would be added as the last question. This is much harder than the previous one, this I can assure”

The students were intrigued, what kind of question would that be? If the previous question nearly made Selene cry, what would the next question be?

Even the professor by the door was curious as to what Damian was cooking.

At this time, another professor went to the room, it was Professor Aisha.

“Did it start yet?” She asked the other professor.

The other professor was surprised as another professor was taking their break time to watch a silly mock test. He replied nonetheless.

“Yes, two questions had already been given, Damian’s about to write the third one.”

“Wow, it’s a surprise that Nathan was able to hold on this long, were the two questions perhaps relatively easy?” Professor Aisha was skeptical.

“The first question was easy, even highschoolers will be able to answer that question. However, it was not the case in the second question, though the question was a straightforward derivative question, Selene had a hard time,” The professor stated.

“It can be understood since she isn’t a mathematics major but how did Nathan answer it, did he cheat?”

“No, no, no, we have two professors here, there’s not a chance he was able to cheat. Besides, he was faster and answered the questions more calmly than Selene.”

“How’s that possible? You know his grades, right?”

“I know, but you also should’ve known of the other rumor that only professors know in our department, right? That his grades have been meticulously crafted by him, if we based it on that then it would answer our question.”

Professor Aisha wanted to reply to his statement but before she could do it, the other professor said to just watch and see the truth with her own eyes.

Professor Damian stood up before saying, “This is a mouthful so It’s better that I just write this instead, you don’t need to write the question itself.”

Question: Let V be a vector space over a field F, and let T: V → V be a linear transformation. Prove or disprove the following statement: If T2 = T 2 =T (where T2 T 2 denotes the composition of T with itself), then T is a projection transformation. Instructions: Provide a rigorous proof if the statement is true, or provide a counterexample and a justification if the statement is false. Ensure to clearly define all terms used in your proof or counterexample.

Professor Aisha and the other professor were shocked, the same thoughts are in their mind, is this mathematics at the level of a first-year college?

The professors are shocked, what more with the other students at the back. They have their jaws wide open; they don’t understand a single thing, they synchronously look at Selene who is also puzzled.

‘There should be a limit on how unreasonable a professor is’ Those are the words that all students in the room have in their minds.

Is Professor Damian a psychopath in the dark?

On the other hand, Warlock was perplexed by another thing. It seems that Nathan appears not too bothered by the question and is currently writing.

The other students now noticed Nathan writing while Selene also watched with them. Nathan was serious on the question and did not notice the gazes of the people, and even if he did notice, he wouldn’t care.

Time passed by and a couple of minutes finally went by, Nathan looked up and saw all of the people in the room looking at him.

“What’s the matter?” He spoke.

The students didn’t speak and waited for Professor Damian to check Nathan’s work.

After comparing the answer along with the solution of the professor to Nathan’s, he said that they all matched. Nathan answered correctly.

The class was in an uproar. The underdog really won against the tides of battle. They were all so sure that Selene would come out on top with the bout but the result said otherwise. They really couldn’t believe it.

“You didn’t cheat, did you?” A classmate of his said. This caught the attention of the other students, the probability of this happening is below 1%, how was Nathan able to answer such a question.

Professor Aisha spoke up amidst the discussion, “Could you care to explain how you arrive at this answer?”

The words of the professor lighten up the mood of the students, they agreed. If Nathan really knows how to solve it then discussing how he came up with the answer shouldn’t be difficult, right?

“I guess that’s fine.” Nathan went to the board and solved it in real time.

Every step he had done, he explained to the rest. After a couple minutes of discussion, they finally accepted it. With how eloquent Nathan explained, there was no doubt that it was indeed him who solved it and did not cheat.