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Matrices Class 10 Maths ICSE Solutions

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Formulae

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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.
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Properties of Matrix Addition:

  1. Matrix addition is commutative
    i.e., A + B = B + A
  2. Matrix addition is associative for any three matrices A, B and C.
    A + (B + C) = (A + B) + C.
  3. Existence of identity.
    A null matrix is identity element for addition.
    i.e., A + 0 = A = 0 + A.
  4. 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).
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Properties of Matrices Multiplication

  1. Matrix multiplication is not commutative in general for any two matrices AB ≠ BA.
  2. Matrix multiplication is associative
    i.e., (AB) C = A (BC) when both sides are defined.
  3. Matrix multiplication is distributed over matrix addition
    i.e., A (B + C) = AB + AC
    (A + B) C = AC + BC.
  4. If A is an n × n matrix then
    InA = A = AIn
  5. The product of two matrices can be the null matrix while neither of them is the null matrix.

Determine the Following

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Prove the Following 

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