Basic Operations of Matrix | Engineering Maths for GATE PSU ESE AE/JE

Matrices are a fundamental part of Engineering Mathematics and are frequently asked in exams like GATE, PSU, ESE, AE/JE.

What is a Matrix?

A matrix is a rectangular array of numbers arranged in rows and columns.

Example:

1	2	3
4	5	6

1. Addition of Matrices

Two matrices can be added only if they have the same order.

Example:

Matrix A:

1	2
3	4

Matrix B:

5	6
7	8

A + B:

6	8
10	12

2. Subtraction of Matrices

A − B:

-4	-4
-4	-4

3. Scalar Multiplication

2 × A:

2	4
6	8

4. Multiplication of Matrices

Matrix A:

1	2
3	4

Matrix B:

5	6
7	8

AB:

19	22
43	50

5. Transpose of a Matrix

Matrix A:

1	2	3
4	5	6

Transpose A^T:

1	4
2	5
3	6

Important Properties

A + B = B + A
(A + B) + C = A + (B + C)
AB ≠ BA
(A^T)^T = A

Exam Tips

Always check matrix order before operations
Practice multiplication carefully
Focus on concept clarity

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