Question

What is the condition that is to be satisfied for the identity (P+Q) (P-Q)=$P^2-Q^2$ to be true for any two square matrices P and Q?

• A. The identity is always true
• B. PQ$\ne$QP
• C. PQ and QP are not null matrices
• D. PQ=QP

Answer 1

The correct option is D PQ=QP

Given $(P-Q)(P-Q)=P^2-Q^2$

$L.H.S$

$(P+Q)(P-Q)=P^2-PQ+QP-Q^2$

If $PQ=QP\Rightarrow (P+Q)(P-Q)=P^2-Q^2$