It describes the various operations on a matrix.

1. Mangalayatan University
12/30/2025 1
Faculty Name :- Prof.
Course Name :- Matrix Theory
Course Code :- CSB – 2213
Semester :- 1
Class No. :- 2
Chapter No :- 1
JULY’2025
SESSION

2. Mangalayatan University
Matrices
Matrix Operations

3. Mangalayatan University
Matrices - Operations
EQUALITY OF MATRICES
Two matrices are said to be equal only when all
corresponding elements are equal
Therefore their size or dimensions are equal as well
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3
2
5
0
1
2
0
0
1










3
2
5
0
1
2
0
0
1
A = B = A = B

4. Mangalayatan University
Matrices - Operations
Some properties of equality:
•IIf A = B, then B = A for all A and B
•IIf A = B, and B = C, then A = C for all A, B and C
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
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
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3
2
5
0
1
2
0
0
1
A = B =
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
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33
32
31
23
22
21
13
12
11
b
b
b
b
b
b
b
b
b
If A = B then ij
ij b
a 

5. Mangalayatan University
Matrices - Operations
ADDITION AND SUBTRACTION OF MATRICES
The sum or difference of two matrices, A and B of the same
size yields a matrix C of the same size
ij
ij
ij b
a
c 

Matrices of different sizes cannot be added or subtracted

6. Mangalayatan University
Matrices - Operations
Commutative Law:
A + B = B + A
Associative Law:
A + (B + C) = (A + B) + C = A + B + C
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
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9
7
2
5
8
8
3
2
4
6
5
1
6
5
2
1
3
7
A
2x3
B
2x3
C
2x3

7. Mangalayatan University
Matrices - Operations
A + 0 = 0 + A = A
A + (-A) = 0 (where –A is the matrix composed of –aij as elements)
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
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1
2
2
2
2
5
8
0
1
0
2
1
7
2
3
2
4
6