Topic explanation

Standard explanation

If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A^-1 = I on one row if time.

Key points

• det first
• invertible <-> det != 0 (square)
• rank = number of pivots
• det=0: stop
• FIND A^-1: If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A^-1
• FIND A^-1: If det=0, stop: no inverse.
• WHAT — FIND A^-1: If det=0, stop: no inverse. 2x2 swap formula. 3x3: row ops on the augmented identity. Check A A^-1
• WHY — Why it matters: This rule is a separate learning unit inside inverse and rank (row operations). It can be defined, a

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