If A is skew symmetric matrix, then A² is a 

CONCEPT:

Symmetric Matrix:

Any real square matrix A = (a_ij) is said to be symmetric matrix if and only if a_ij = a_ji, ∀ i and j or in other words we can say that if A is a real square matrix such that A = A^t then A is said to be a symmetric matrix.

Skew-symmetric Matrix:

Any real square matrix A = (a_ij) is said to be skew-symmetric matrix if and only if a_ij = - a_ji, ∀ i and j or in other words we can say that if A is a real square matrix such that A = - A^t then A is said to be a skew-symmetric matrix.

Properties of Transpose of a Matrix:

• If A is a matrix of order m × n, then (A^t)^t = A
• If k ∈ R is a scalar and A is a matrix of order m × n, then (k × A)^t = k × A^t
• If A and B are matrices of same order m × n, then (A ± B)^t = A^t ± B^t.

CALCULATION:

Given: A is skew symmetric matrix

As we know that, if A is a skew symmetric matrix i.e A = - At 

⇒ (A²)^t = (A^t)²

∵ A is skew symmetric matrix

⇒ (A2)t = (- A)² = A²

So, A² is a symmetric matrix.

Hence, option D is the correct answer.