99 Percentile Qs Bank for JEE MainMathematicsMatrices

Let A x = 0 x - 2 x - 3 x + 2 0 x - 5 x + 3 x + 5 0 , then the matrix A 0 A 0 T is a

Options

Anull matrix
Bsymmetric matrix
Cskew symmetric matrix
Dnon singular matrix

Correct answer

B. symmetric matrix

Step-by-step solution

A 0 = 0 - 2 - 3 2 0 - 5 3 5 0 A 0 T = 0 2 3 - 2 0 5 - 3 - 5 0 = - A 0 ⇒ A 0 is a skew-symmetric matrix A 0 A 0 T T = A 0 T T A 0 T = A 0 A 0 T ⇒ A 0 A 0 T is a symmetric matrix Also, A 0 A 0 T = A 0 2 = 0

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