Question

Under what condition is the matrix equation $A^2-B^2=(A-B)(A+B)$ is true ?

• A. $AB=BA$
• B. $AB\ne BA$
• C. $A=B$
• D. $A-B=AB$

Answer 1

Answer: (A), (C)

$AB=BA$
$A=B$

We have,

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

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

$A^2-B^2=A^2-BA+AB-B^2$

$O=A^2-BA+AB-B^2-A^2+B^2$

$O=-BA+AB$

$AB=BA$

So A and C are correct answers .