Matrix

Matrix is a topic where a grid of numbers or letters is given and you have to find the missing value by identifying the pattern or rule that connects the rows and columns. It is a quick scoring topic in SSC CGL Reasoning.

What is a Matrix?

A matrix is simply a table arranged in rows and columns. In SSC CGL, matrices are usually 3x3 grids (3 rows and 3 columns) containing numbers or letters.

Example of a 3x3 Matrix:

| 2  | 4  | 8  |
| 3  | 9  | 27 |
| 4  | 16 | ?  |

Answer: 64 (each row follows the pattern: first number, its square, its cube)

Types of Matrix Questions in SSC CGL:

Type 1 - Row Pattern The pattern works across each row.

Example:

| 3  | 6  | 9  |
| 4  | 8  | 12 |
| 5  | 10 | ?  |

Logic: In each row the second number = first × 2, third number = first × 3. Answer: 15

Type 2 - Column Pattern The pattern works down each column.

Example:

| 5  | 10 | 15 |
| 6  | 12 | 18 |
| 7  | 14 | ?  |

Logic: In each column the numbers increase by 1 going down. Third column: 15, 18, 21. 

Answer: 21

Type 3 - Diagonal Pattern The pattern works along the diagonal of the matrix.

Example:

| 1  | 2  | 3  |
| 4  | 5  | 6  |
| 7  | 8  | ?  |

Logic: Numbers are simply consecutive. After 8 comes 9. 

Answer: 9

Type 4 - Operation Based Pattern A mathematical operation connects numbers in each row or column.

Example:

| 4  | 5  | 20 | | 3  | 7  | 21 | | 6  | 8  | ?  |

Logic: First number × second number = third number. 6 × 8 = 48. Answer: 48

Type 5 - Letter Matrix Letters instead of numbers follow a positional pattern.

Example:

| 4  | 5  | 20 |
| 3  | 7  | 21 |
| 6  | 8  | ?  |

Logic: Each row starts one letter after the previous row. Third row starts at C, so C, E, G. Answer: G

Common Patterns Used in Matrix Questions:

• Addition: Each number in a row/column increases by a fixed value
• Multiplication: Each number is multiplied by a fixed value
• Squares and Cubes: Numbers follow square or cube patterns
• Sum of row: The third number equals sum of first two
• Product of row: The third number equals product of first two
• Difference: Third number equals difference of first two
• Mixed operations: Combination of two operations

How to Solve Matrix Questions:

Step 1 - Look at the complete rows and columns first (the ones without missing values). 

Step 2 - Find the pattern in those complete rows/columns. 

Step 3 - Apply the same pattern to the row/column with the missing value. 

Step 4 - Always verify your answer by checking it against another row or column. 

Step 5 - If row pattern does not work, try column pattern or diagonal pattern.

Important Tips:

• Always start with complete rows/columns - never start with the row that has the missing value
• Check at least 2 rows/columns before concluding the pattern
• In letter matrices, convert letters to position numbers first
• Most SSC CGL matrix questions use simple operations - do not overthink
• Practice 10 matrix questions daily - this topic takes only 30 seconds per question
• 1 to 2 questions come from this topic in SSC CGL every year