If A and B are two matrices of order 2 × 2 such that A is a symmetric matrix and B is a skew-symmetric matrix, then:

$A^2$ is also a symmetric matrix

The correct answer is Option (1) → $A^2$ is also a symmetric matrix

For any symmetric matrix $A$, $A^T=A$.

$(A^2)^T=(AA)^T=A^TA^T=AA=A^2$, so $A^2$ is symmetric ✅

For any skew-symmetric matrix $B$, $B^T=-B$.

$(B^2)^T=(BB)^T=B^TB^T=(-B)(-B)=BB=B^2$, so $B^2$ is symmetric, not skew-symmetric ❌

$A+B$ cannot be an identity matrix in general ❌

$A-B$ cannot be a null matrix in general ❌

Correct answer: $A^2$ is also a symmetric matrix.