Exercise 1: G x H vs. H x G — Possible Solution
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GIVEN
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G = [[2, 0], [1, 3]]
H = [[4, 1], [2, 5]]

STEP 1: COMPUTING G x H
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Row 0, Col 0: (2)(4) + (0)(2) = 8 + 0   = 8
Row 0, Col 1: (2)(1) + (0)(5) = 2 + 0   = 2
Row 1, Col 0: (1)(4) + (3)(2) = 4 + 6   = 10
Row 1, Col 1: (1)(1) + (3)(5) = 1 + 15  = 16

G x H = [[8, 2], [10, 16]]

STEP 2: COMPUTING H x G
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Row 0, Col 0: (4)(2) + (1)(1) = 8 + 1   = 9
Row 0, Col 1: (4)(0) + (1)(3) = 0 + 3   = 3
Row 1, Col 0: (2)(2) + (5)(1) = 4 + 5   = 9
Row 1, Col 1: (2)(0) + (5)(3) = 0 + 15  = 15

H x G = [[9, 3], [9, 15]]

STEP 3: CONFIRMING THE TWO RESULTS DIFFER
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G x H = [[8, 2], [10, 16]]
H x G = [[9, 3], [9, 15]]

Every single entry differs between the two results, confirming this
chapter's own non-commutativity claim directly with a concrete example
rather than taking it on faith.

WHY THIS WORKS AS AN ANSWER
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Each entry of both products is computed from this chapter's own row-
by-column dot-product rule, shown individually rather than skipped,
and the two full results are compared entry by entry to explicitly
confirm G x H does not equal H x G.