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NDA 2 2024 Maths, question 49

Topic: Matrices and determinants

Passage · Q49 to Q50

Let A=[3−342−340−11]A=\begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}

Q49

What is A(adjA)A(\text{adj}A) equal to?

  1. (a) [500050005]\begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}
  2. (b) [200020002]\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix}
  3. (c) [1/20001/20001/2]\begin{bmatrix} 1/2 & 0 & 0 \\ 0 & 1/2 & 0 \\ 0 & 0 & 1/2 \end{bmatrix}
  4. (d) [100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}Correct answer

Solution.

Answer: (d) [100010001]\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}

  1. For every square matrix, A adj A=(det A)I.
  2. Expand the given determinant: 3(−3+4)+3(2)+4(−2)=1.
  3. Hence the product is I₃, option (d).