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

Consider the following in respect of matrices A and B of same order: 1. A ^2- B ^2=( A + B )( A - B ) 2. (A-I)(I+A)=0 A^2=I Where I is the identity matrix and O is the null matrix. Which of the above is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

B. 2 only

Step-by-step solution

Matrix product is commutative if both are diagonal matrices of same order. A ^2- B ^2=( A + B )( A - B ) is not true. Next, ( A - I )( A + I )=0 A ^2+ AI - IA - I ^2=0( AI = IA ) A ^2= I is 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