Exercise 1: Why "HELLO" -match "hello" Is True — Possible Solution
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WHY IT RETURNS $true
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Per this chapter, -match is case-INSENSITIVE by default, exactly like every comparison operator introduced back in Fundamentals 4 (-eq, -like, and the rest). "HELLO" and "hello" differ only in letter case, and since -match ignores case differences by default, it reports a successful match despite the two strings not being an exact character-for-character match.

THE CONNECTION TO -eq
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This mirrors Fundamentals 4's own -eq behavior directly - PowerShell's comparison operators are consistently case-insensitive by default across the board, not just for -match specifically. It's a single, consistent design choice applied uniformly across the whole operator family, not a special exception carved out just for regex matching.

THE CASE-SENSITIVE ALTERNATIVE
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-cmatch is the case-sensitive variant of -match, per this chapter. "HELLO" -cmatch "hello" would return $false, since the case-sensitive form requires an exact case match rather than ignoring case differences.

WHY THIS WORKS AS AN ANSWER
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It correctly explains that -match is case-insensitive by default, correctly ties this back to Fundamentals 4's own -eq behavior as the same underlying design pattern, and correctly names -cmatch as the case-sensitive alternative.