Show that if A and B are square matrices such that AB = BA, then … - Vidyadip

Question

Show that if A and B are square matrices such that AB = BA, then (A + B)² = A² + 2AB + B².

✓

Answer

Since, A and B are square matrices such that AB = BA

$\therefore$ (A + B)² = (A + B).(A + B)

= A² + AB + BA + B²

= A² + AB + AB + B² $[\because$ AB = BA$]$

= A² + 2AB + B²

Hence proved.

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