(a) True. Suppose A is a not a square matrix, with m rows and n columns. Then A² is not defined, because you can't multiply an m×n matrix by another m×n matrix.
(b) False. As an example, consider the matrices


Then both AB and BA are defined, with


In general, you can multiply any m×n by any n×m matrix.
(c) True. Multiplying a m×n matrix by a n×m matrix always yields a m×m matrix, and multiplying a n×m matrix by a m×n matrix always yields a n×n matrix.
The function that represents the Scooter Company's total profit is given by:
P(x) = -2x² + 250x - 2,000.
<h3>How to calculate the profit function?</h3>
The profit function is calculated by the <u>revenue function subtracted by the cost function</u>, hence:
P(x) = R(x) - C(x).
In this problem, we have that:
- The revenue function is: R(x) = 400x - 2x².
- The cost function is: X(x) = 150x + 2000.
Hence the profit function is:
P(x) = R(x) - C(x).
P(x) = 400x - 2x² - (150x + 2000).
P(x) = -2x² + 250x - 2,000.
More can be learned about profit functions at brainly.com/question/25274969
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