Question: Is it true that det(A + B) = det A + det B? Experiment with four pairs of random matrices as in Exercise 48, and

Is it true that det(A + B) = det A + det B? Experiment with four pairs of random matrices as in Exercise 48, and make a conjecture.

Data from in Exercise 48

Is it true that det AB = (det A) (det B)? To find out, generate random 5 x 5 matrices A and B, and compute det AB - (det A det B). Repeat the calculations for three other pairs of n x n matrices, for various values of n. Report your results.

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