Tamil Nadu Board of Secondary EducationHSC Arts Class 12

Choose the correct alternative: If A B, and C are invertible matrices of some order, then which one of the following is not true? - Mathematics

Advertisements
Advertisements
MCQ

Choose the correct alternative:

If A B, and C are invertible matrices of some order, then which one of the following is not true?

Options

  • adj A = |A|A1

  • adj(AB) = (adj A)(adj B)

  • det A–1 = (det A)1

  • (ABC)1 = C1B1A1

Advertisements

Solution

adj(AB) = (adj A)(adj B)

Concept: Inverse of a Non-singular Square Matrix
  Is there an error in this question or solution?
Chapter 1: Applications of Matrices and Determinants - Exercise 1.8 [Page 48]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 1 Applications of Matrices and Determinants
Exercise 1.8 | Q 9 | Page 48

RELATED QUESTIONS

Find the adjoint of the following:`1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]`


Find the inverse (if it exists) of the following:

`[(-2, 4),(1, -3)]`


If `"F"(alpha) = [(cosalpha, 0, sinalpha),(0, 1, 0),(-sinalpha, 0, cosalpha)]`, show that `["F"(alpha)]^-1 = "F"(- alpha)`


If A = `[(3, 2),(7, 5)]` and B = `[(-1, -3),(5, 2)]`, verify that (AB)–1 = B1 A1 


If adj(A) = `[(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`, find A–1 


Find adj(adj(A)) if adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 1)]`


A = `[(1, tanx),(-tanx, 1)]`, show that AT A–1 = `[(cos 2x,  - sin 2x),(sin 2x, cos 2x)]`


Find the matrix A for which A`[(5, 3),(-1, -2)] = [(14, 7),(7, 7)]`


Given A = `[(1, -1),(2, 0)]`, B = `[(3, -2),(1, 1)]` and C = `[(1, 1),(2, 2)]`, find a martix X such that AXB = C


If A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]`, show that `"A"^-1 = 1/2("A"^2 - 3"I")`


Decrypt the received encoded message [2 – 3][20 – 4] with the encryption matrix `[(-1, -1),(2, 1)]` and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 – 26 to the letters A – Z respectively, and the number 0 to a blank space


Choose the correct alternative:

If |adj(adj A)| = |A|9, then the order of the square matrix A is


Choose the correct alternative:

If A is a 3 × 3 non-singular matrix such that AAT = AT A and B = A-1AT, then BBT =


Choose the correct alternative:

If A = `[(2, 0),(1, 5)]` and B = `[(1, 4),(2, 0)]` then |adj (AB)| =


Choose the correct alternative:

Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj (A).
(iv) A(adj A) = (adj A)A = |A|I


Choose the correct alternative:

If A = `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]`, then adj(adj A) is


Share
Notifications



      Forgot password?
Use app×