Question

Idempotent matrix is also skew symmetric then it must be what

Answer 1

Since the options are not given, I am giving a general answer.

The correct answer should be - Square matrix.

An Idempotent matrix is symmetric or a skew-symmetric matrix.

Consider that M is a matrix, so, it's skew-symmetric matrix will be M' = −M.

Let M be an m x n matrix. Then, by definition, M' will be denoted as an n x m matrix, and therefore −M will also be n x m.

Since M = −M', the dimensions of −M should be the same as that of M. So, m × n must be similar to n x m. This way we can say that m = n.

Therefore, M can also be denoted as n x n, which makes M a square matrix.