Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main2006MathematicsMatricesActual

If A and B are square matrices of size n n such that A^2-B^2=(A-B)(A+B) , then which of the following will be always true?

Options

  1. AA = B
  2. BAB = BA
  3. Ceither of A or B is a zero matrix
  4. Deither of A or B is an identity matrix

Correct answer

B. AB = BA

Step-by-step solution

A^2-B^2=(A-B)(A+B)A^2-B^2=A^2+A B-B A-B^2 A B=B A

Practice Matrices on Quantrex Academy →

More from Matrices

Which one of the following matrices can be obtained by performing elementary row transformations on the 3 3 identity matrix? 2026Consider the matrix M = bmatrix 2 & -1 1 & 0 bmatrix . Let p, q, r, s, a, b, c and d be integers such that M²⁶ = bmatrix p & q r & s bmatrix and _ k=1 ²⁶ M^k = bmatrix a & b c & d 2026For real numbers , , , and , consider the matrix M = bmatrix & 1 2 & - 1 2 1 3 & & 1 3 & & bmatrix . Suppose that MM^T = I , where M^T is the transpose of the matrix M , and I is t 2026Let R denote the set of all real numbers and let i = -1 . Consider the matrices S = bmatrix 0 & -1 1 & 0 bmatrix and T = bmatrix 1 & 1 0 & 1 bmatrix . Let a, b, c, d be real number 2026Let A = bmatrix & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5 & 0 0 & 4 & -2 bmatrix + adj (A) . If (B)=66 , then ( adj (A)) equals: 2026Let A = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and B = [b_ ij ] , 1 i, j 3 . If B = A⁹⁹ - I , then the value of b₃₁ - b₂₁ b₃₂ is : 2026Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + (adj(adj(A))) + (adj(A)(adj(adj(A)))) = bmatrix 2 & -2 & 2 -2 & 0 & -1 0 & 0 & -1 bmatrix for some , R . Then 2026Let M be a 3 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M pmatrix 0 1 0 pmatrix = pmatrix 0 1 2 pmatrix and M pmatrix 0 0 1 pmatrix = pmatrix -1 1 1 pmatr 2026 Full Matrices list All JEE Main PYQs