Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2024MathematicsMatricesActual

Let A and B be two square matrices of same order. If A B is a null matrix, then which one of the following is correct?

Options

  1. ABoth A and B are null matrices
  2. BEither A or B is a null matrix
  3. CB is a null matrix if A is a non-singular matrix
  4. DBoth A and B are singular matrices

Correct answer

C. B is a null matrix if A is a non-singular matrix

Step-by-step solution

We have, AB =0 Let A= [ array ll a & b c & d array ] and B= [ array ll p & q r & s array ] So, AB = [ array ll a & b c & d array ] [ array ll p & q r & s array ]= [ array ll 0 & 0 0 & 0 array ] [ array ll ap + br & aq + bs cp + dr & cq + ds array ]= [ array ll 0 & 0 0 & 0 array ] Comparing both sides, we have aligned & ap + br =0 ....(i) & aq + bs =0 ....(ii) & cp + dr =0 ....(iii) & cq + ds =0 ....(iv) aligned Solving equation (i) and (iii), we get ( ad - bc ) p =0 and ( ad - bc ) r =0 Solving equation (ii) amd (i

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