Which of the following is incorrect - Vidyadip

MCQ

Which of the following is incorrect

✓
${A^2} - {B^2} = (A + B)(A - B)$
B
${({A^T})^T} = A$
C
${(AB)^n} = {A^n}{B^n},$where $A, B$ commute
D
$(A - I)(I + A) = O \Leftrightarrow {A^2} = I$

✓

Answer

Correct option: A.

${A^2} - {B^2} = (A + B)(A - B)$

a
(a) We have $(A + B)(A - B) = {A^2} - AB + BA - {B^2}$

$\therefore$ Option $(a)$ is not true.

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