Number Matrix

Number Matrix problems present a 3×3 matrix of numbers and ask for the sum, product, or other operation on specific elements. Common calculations include sum of main diagonal, sum of anti-diagonal, sum of all corners, sum of middle row or column, and product of diagonal elements. These problems test basic arithmetic operations applied to matrix positions.

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Introduction to Number Matrix

Number Matrix problems present a 3×3 matrix of numbers and ask for the sum, product, or other operation on specific elements. Common calculations include sum of main diagonal, sum of anti-diagonal, sum of all corners, sum of middle row or column, and product of diagonal elements. These problems test basic arithmetic operations applied to matrix positions.

Prerequisites

Matrix indexing (row, column) Basic arithmetic (addition, multiplication) Diagonal identification Corner identification
Why This Matters: Number Matrix problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test matrix arithmetic and position identification.

How to Solve Number Matrix Problems

1

Step 1: Identify the positions of elements to be included (e.g., main diagonal, corners)

2

Step 2: For main diagonal: elements where row = column (positions (1,1), (2,2), (3,3))

3

Step 3: For anti-diagonal: elements where row + column = 4 (positions (1,3), (2,2), (3,1))

4

Step 4: For corners: positions (1,1), (1,3), (3,1), (3,3)

5

Step 5: For middle row: positions (2,1), (2,2), (2,3)

6

Step 6: For middle column: positions (1,2), (2,2), (3,2)

7

Step 7: Perform the required operation (sum or product) on the identified elements

8

Step 8: Present the result

Pro Strategy: First identify which positions are being asked. Use the formulas: main diagonal: i=j; anti-diagonal: i+j = n+1 (where n=3 for 3×3); corners: (1,1), (1,n), (n,1), (n,n). Then perform the arithmetic operation.

Example Problem

Example: Matrix: 1 2 3 4 5 6 7 8 9 What is the sum of the main diagonal? Solution: Step 1: Main diagonal elements: (1,1)=1, (2,2)=5, (3,3)=9 Step 2: Sum = 1 + 5 + 9 = 15 Answer: 15

Pro Tips & Tricks

  • Main diagonal positions: (1,1), (2,2), (3,3) for 3×3 matrix
  • Anti-diagonal positions: (1,3), (2,2), (3,1)
  • Corners: (1,1), (1,3), (3,1), (3,3)
  • Middle row: (2,1), (2,2), (2,3)
  • Middle column: (1,2), (2,2), (3,2)
  • Sum of all elements in 3×3 matrix = 1+2+3+4+5+6+7+8+9 = 45

Shortcut Methods to Solve Faster

For a 3×3 matrix with numbers 1-9 in order: main diagonal sum = 15, anti-diagonal sum = 15, all corners sum = 20
Sum of middle row = 4+5+6 = 15, middle column = 2+5+8 = 15
Product of main diagonal = 1×5×9 = 45
Sum of all elements = (n³ + n)/2 for n=3 → (27+3)/2 = 15? Actually 1+9=10, 2+8=10, 3+7=10, 4+6=10, +5=45

Common Mistakes to Avoid

Confusing main diagonal with anti-diagonal
Including the wrong positions for corners
Forgetting that middle row and middle column share the center element
Using multiplication when addition is asked (or vice versa)

Exam Importance

Number Matrix is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
INSURANCE
1-2 questions

Ready to Master Number Matrix?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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