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Most Important Selected Qs for JEE AdvancedMathematicsMatrices

Which of the following is/are true:

Options

  1. AIf A and B are two singular matrix then their product AB is null matrix.
  2. BIf A B is null matrix, where A & B are non-zero matrices then A and B are singural matrices.
  3. CA is a non-singular square matrix of order n n and k is a scalar, then |adj kA is equal to k ^ n ^2- n |A|^ n-
  4. D| adj ( adj A)|=| A |^ n ^2-1

Correct answer

C. A is a non-singular square matrix of order n n and k is a scalar, then |adj kA is equal to k ^ n ^2- n |A|^ n-

Step-by-step solution

(A) False (B) True (C) True, | adj K A|=|K A|^ n-1 =K^ n^2-n |A|^ n-1 (D) | adj ( adj A)|=| A |^ ( n -1)^2

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