Question

If A and B are square matrices of the same order, explain, why in general

 (A + B) (A − B) ≠ A² − B²

Answer 1

\[\left( iii \right) LHS = \left( A + B \right)\left( A - B \right)\]

\[ = A\left( A - B \right) + B\left( A - B \right)\]

\[ = A^2 - AB + BA - B^2\]

We know that a matrix does not have commutative property. So,
AB ≠ BA
Thus, 

\[\left( A + B \right)\left( A - B \right)\]≠

\[A^2 - B^2\]