Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2018MathematicsMatricesActual

Consider the following in respect of matrices A , B and C of same order: 1. ( A + B + C )^ = A ^ + B ^ + C ^ 2. ( AB )^ = A ^ B ^ 3. ( ABC )^ = C ^ B ^ A ^ Where A ^ is the transpose of the matrix A . Which of the above are correct?

Options

  1. A1 and 2 only
  2. B2 and 3 only
  3. C1 and 3 only
  4. D1,2 and 3

Correct answer

C. 1 and 3 only

Step-by-step solution

By property, statement 1 and 3 are correct.

Practice Matrices on Quantrex Academy →

More from Matrices

Consider the following statements : I. If n n(n>1) matrix is symmetric, then its inverse is also a symmetric matrix. II. If n n(n>1) matrix is singular, then its adjoint is also a 2026If M is a square matrix such that M^3=M , then how many values of |M| are possible ? 2026If M_k= bmatrix k & k-1 k-1 & k bmatrix where k is a natural number, then what is |M₁|+|M₂|+|M₃|+ +|M₅₀| equal to ? 2026If M^ T is the transpose of a 2 2 matrix M , then which of the following is/are correct ? I. |M+M^ T |=|M|+|M^ T | if M is symmetric. II. |M+M^ T |=0 if M is anti-symmetric. Select 2026Consider the following in respect of non-singular matrices A and B : I. (AB)⁻¹ = A⁻¹B⁻¹ II. (BA)(AB)⁻¹ = I , where I is the identity matrix III. (AB)^T = A^T B^T How many of the ab 2025For the following two (02) items: Let A = pmatrix & - & pmatrix . What is [ adj , A]⁻¹ equal to? 2025Consider the following statements about the matrix M = pmatrix 71 & 23 & 48 57 & 28 & 29 65 & 17 & 48 pmatrix : Statement-I: The inverse of M does not exist. Statement-II: M is non 2025If [x 1 1] pmatrix 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 pmatrix pmatrix 1 1 x pmatrix = [45] , then which one of the following is a value of x ? 2025 Full Matrices list All NDA PYQs