MHT-CET : Mathematics Entrance Exam

### MHT - CET : Mathematics - Matrices Formulae Page 1

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1. Equality of Two Matrices:

 If A = [aij] and B = [bij]are the two matrices of same order then they are said to be equal if their corresponding elements are same. i.e., A = B if aij =bij for all i and j.

2. Addition and Subtraction of Two Matrices:

 If A = [aij]m ´ n and B = [bij]m ´ n then A + B = [aij + bij]m ´ n and A – B= [aij – bij]m ´ n for all i and j.

3. If A, B, C are three matrices of same order, then

 (i) A + B = B + A, Commutative law. (ii) A + (B + C) = (A + B) + C, Associative law (iii) A + 0 = 0 + A = A, where 0 is a null matrix

4. Multiplication of two Matrices:

 If A = [aij]m ´ n and B = [bjk]n ´ p are two matrices then the product C = AB = [Cik]m ´ n where Cik can be obtained by multiplying the ith row of A and kth column of B.

5. Properties of Matrix Multiplication :

If A, B, C are three matrices, then

·

AB ¹ BA (in general)

·

A(BC) = (AB)C, associative law.

·

 A(B + C) = AB + AC (A + B)C = AC + BC distributive law.

·

A.0 = 0.A = 0, where 0 is a null matrix.

·

A.I = I.A = A, where I is an identity matrix.

6. Properties of Transpose :

 If A and B are two matrices and k is a scalar, then

7. Some useful results:

8. Some useful properties:

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