We have, A and B are two non-square matrices such that P=A+B,Q=ATB,R=ABT Since, A+B is defined, So order of A and B are same. Let order of A and B be m×n ∴ Order of AT is n×m and order of BT is n×m Now, order of P= order of A+B=m×n Order of Q= order of ATB=n×n And order of R= order of ABT=m×m Now, order of PQ=m×n Order of QR= not defined Order of RQ= not defined Order of QP= not defined Order of RP=m×n ∴ Order of A= order of PQ and RP