What is not true for a skew-symmetric matrix?

Solution : Every skew symmetric matrix of odd order is singular. So option (a) is incorrect.

What is the condition for skew-symmetric matrix?

The two important conditions for a matrix to be skew symmetric are that it should be a square matrix i.e., the number of rows and columns should be equal and secondly, the given matrix should be equal to the negative of its transpose.

Can a skew-symmetric matrix be nonsingular?

Considerable attention is devoted to properties of sign-nonsingular skew-symmetric matrices A = (aij) for which there do not exist sign-nonsingular skew-symmetric matrices B = (bij) of the same order with more nonzero entries and aij = 0 whenever bij = 0.

Is a skew symmetric matrix?

A matrix is symmetric if and only if it is equal to its transpose. All entries above the main diagonal of a symmetric matrix are reflected into equal entries below the diagonal. A matrix is skew-symmetric if and only if it is the opposite of its transpose. All main diagonal entries of a skew-symmetric matrix are zero.

What is the determinant of skew symmetric matrix of even order?

Det of a skew symmetric matrix of even order is a non-zero perfect square.

Is it said to be skew-symmetric matrix?

A matrix is skew-symmetric if and only if it is the opposite of its transpose. All main diagonal entries of a skew-symmetric matrix are zero.

Is diagonal elements of a skew-symmetric matrix is?

A scalar multiple of a skew-symmetric matrix is skew-symmetric. The elements on the diagonal of a skew-symmetric matrix are zero, and therefore its trace equals zero. , i.e. the nonzero eigenvalues of a skew-symmetric matrix are non-real.

Does det A det (- A?

If A is an n×n square matrix and n is odd, then det(−A)=−det(A).

What is the determinant of a skew Hermitian matrix?

The determinant of an even order skew-Hermitian matrix with complex entries is always a real number. (D-bar)={(-1)^(2m)}D, where bar denotes complex conjugate, and this operation preserves sum and products, and D = det(A). Hence we get D bar = D, i.e. D is real.