![Q.17 If P = [ 1 1 2 2 ], Q = [ 2 1 2 2 ] and R = [ 3 0 1 3 ], which one of the following statements is TRUE? PQ = PR QR = RP QP = RP PQ = QR](https://www.letstalkacademy.com/wp-content/uploads/2026/01/slide_17-3.jpg)
Q.17 If
P =
[ 1 1
2 2 ],
Q =
[ 2 1
2 2 ]
and
R =
[ 3 0
1 3 ],
which one of the following statements is TRUE?
- PQ = PR
- QR = RP
- QP = RP
- PQ = QR
Introduction
Matrix multiplication is an important topic in linear algebra and is frequently tested in competitive
examinations such as GATE, IIT-JAM, and CSIR-NET. One key property is that matrix multiplication is
not commutative, meaning AB ≠ BA in general.
Given Matrices
P =
[ 1 1
2 2 ]
,
Q =
[ 2 1
2 2 ]
,
R =
[ 3 0
1 3 ]
Step-by-Step Solution
1. Calculation of PQ
PQ =
[ 1 1
2 2 ]
×
[ 2 1
2 2 ]
=
[ 4 3
8 6 ]
2. Calculation of PR
PR =
[ 1 1
2 2 ]
×
[ 3 0
1 3 ]
=
[ 4 3
8 6 ]
Thus, PQ = PR
3. Calculation of QR
QR =
[ 2 1
2 2 ]
×
[ 3 0
1 3 ]
=
[ 7 3
8 6 ]
4. Calculation of RP
RP =
[ 3 0
1 3 ]
×
[ 1 1
2 2 ]
=
[ 3 3
7 7 ]
Final Answer
Correct Option: (A) PQ = PR
Key Takeaways
- Matrix multiplication is order-dependent
- Always compute products explicitly
- Equal matrix sizes do not guarantee equal results
