52. If
A =
| 4 | 2 |
| 1 | 3 |
then A2 + 3A will be
Step 1: Compute A2
A2 = A Β· A
=[4Β Β 2
1Β Β 3]Γ
[4Β Β 2
1Β Β 3]
=[4Β Β 2
1Β Β 3]Γ
[4Β Β 2
1Β Β 3]
Matrix multiplication:
A2 =[18Β Β 14
7Β Β 11]
7Β Β 11]
Step 2: Compute 3A
3A = 3 Γ[4Β Β 2
1Β Β 3]
=[12Β Β 6
3Β Β 9]
1Β Β 3]
=[12Β Β 6
3Β Β 9]
Step 3: Add A2 + 3A
A2 + 3A =
[18Β Β 14
7Β Β 11]
+
[12Β Β 6
3Β Β 9]
[18Β Β 14
7Β Β 11]
+
[12Β Β 6
3Β Β 9]
=[30Β Β 20
10Β Β 20]
Correct Answer
β
Option (A)
[30Β Β 20
10Β Β 20]
Why Other Options Are Incorrect
Option (B): Results from incorrect matrix multiplication.
Option (C): Arithmetic errors during matrix addition.
Option (D): Represents incomplete or incorrectly scaled computation.
Exam Tip
Always calculate matrix powers first, then apply scalar multiplication,
and finally add matrices element-wise to avoid mistakes.
