Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2020MathematicsDeterminants

If A and B are square matrices of same order and B is a skew symmetric matrix, then A^ B A is

Options

  1. ASymmetric matrix
  2. BNull matrix
  3. CDiagonal matrix
  4. DSkew symmetric matrix

Correct answer

D. Skew symmetric matrix

Step-by-step solution

Given B is skew-symmetric matrix gathered B^ =-B (A^ B A )^ =A^ B^ A=A^ (-B) A=- (A^ B A ) gathered A^ B A is skew symmetric matrix.

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025 Full Determinants list All KCET PYQs