By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 1

Topic: Matrices and determinants

Q1

Let XX be a matrix of order 3×33\times 3, YY be a matrix of order 2×32\times 3 and ZZ be a matrix of order 3×23\times 2. Which of the following statements are correct?

I. (ZY)X(ZY)X is defined and is a square matrix of order 33.

II. Y(XZ)Y(XZ) is defined and is a square matrix of order 22.

III. X(YZ)X(YZ) is not defined.

Select the answer using the code given below.

  1. (a) I and II only
  2. (b) II and III only
  3. (c) I and III only
  4. (d) I, II and IIICorrect answer

Solution.

Answer: (d) I, II and III

  1. Matrix multiplication requires matching inner dimensions.
  2. ZY is 3×3, so (ZY)X is 3×3.
  3. XZ is 3×2, so Y(XZ) is 2×2.
  4. YZ is 2×2 and cannot be multiplied on the left by the 3×3 matrix X.
  5. All three statements are correct.