Matrices are a fun way to stretch the mind. They are easy to grasp yet very dissimilar to numbers. Sometimes they can be used to represent numbers and we can use our matrix intuition to answer questions about regular numbers.
You can define functions on matrices just like you define them on numbers. Multiplication is a function. The determinant is a function. You can even take derivatives of these functions. The derivative of the determinant function is written in terms of the trace of the matrix. Yet another matrix function. Who would have guessed that the derivative and trace are related in this way? There's really a lot of depth here.
Don't forget the matrix exponential which might certainly blow the mind of a lot of people here. Matrices as exponent - who would have thought that possible!
You can define functions on matrices just like you define them on numbers. Multiplication is a function. The determinant is a function. You can even take derivatives of these functions. The derivative of the determinant function is written in terms of the trace of the matrix. Yet another matrix function. Who would have guessed that the derivative and trace are related in this way? There's really a lot of depth here.
https://en.wikipedia.org/wiki/Jacobi%27s_formula