ICSE Solutions for Class 10 Mathematics – Matrices
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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
InA = A = AIn
- 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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