**ICSE Solutions for Class 10 Mathematics – Matrices**

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Get ICSE Solutions for Class 10 Mathematics Chapter 10 Matrices for ICSE Board Examinations on ../. We provide step by step Solutions for ICSE Mathematics Class 10 Solutions Pdf. You can download the Class 10 Maths ICSE Textbook Solutions with Free PDF download option.

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**Formulae**

**Addition of Matrices:** Let A and B be two matrices each of order m × n. Then their sum A + B is a matrix of order m × n and is obtained by adding the corresponding elements of A and B.

**Properties of Matrix Addition:**

- Matrix addition is commutative

i.e., A + B = B + A - Matrix addition is associative for any three matrices A, B and C.

A + (B + C) = (A + B) + C. - Existence of identity.

A null matrix is identity element for addition.

i.e., A + 0 = A = 0 + A. - Cancelation laws hold good in case of matrices.

A + B = A + C ⇒ B = C.

**Subtraction of Matrices:**

For two matrices A and B of the same order, we define

A – B = A + (- B).

**Properties of Matrices Multiplication**

- Matrix multiplication is not commutative in general for any two matrices AB ≠ BA.
- Matrix multiplication is associative

i.e., (AB) C = A (BC) when both sides are defined. - Matrix multiplication is distributed over matrix addition

i.e., A (B + C) = AB + AC

(A + B) C = AC + BC. - If A is an n × n matrix then

I_{n}A = A = AI_{n} - The product of two matrices can be the null matrix while neither of them is the null matrix.

**Determine the Following**

**Prove the Following **

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