52. If
A =
| 4 | 2 |
| 1 | 3 |
then A2 + 3A will be
Step 1: Compute A2
A2 = A · A
=[4 2
1 3]Ã
[4 2
1 3]
=[4 2
1 3]Ã
[4 2
1 3]
Matrix multiplication:
A2 =[18 14
7 11]
7 11]
Step 2: Compute 3A
3A = 3 Ã[4 2
1 3]
=[12 6
3 9]
1 3]
=[12 6
3 9]
Step 3: Add A2 + 3A
A2 + 3A =
[18 14
7 11]
+
[12 6
3 9]
[18 14
7 11]
+
[12 6
3 9]
=[30 20
10 20]
Correct Answer
â
Option (A)
[30 20
10 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.
