Matrix Properties

If A and B are symmetric matrices of the same order, then AB is symmetric if

If A is a skew-symmetric matrix of odd order, then |A| equals

The area of the triangle with vertices at the points (1, 2), (4, 6) and (7, 2) in the coordinate pla...

Let A be the two by two matrix with rows (2, 1) and (1, 2); using the Cayley-Hamilton theorem, the m...

For any skew-symmetric matrix of odd order, the determinant always takes a fixed value; the determin...

The homogeneous system of equations with coefficient matrix rows (1, 2, 3), (2, k, 6) and (1, 1, 1) ...

The value of the real parameter k for which the matrix with rows (k, 2, 3), (2, k, 1) and (3, 1, k) ...

If A and B are square matrices of order 3 with det(A) = 3 and det(B) = -2, then the determinant of t...

A square matrix A is called idempotent when it satisfies A squared equal to A; for such a matrix the...

If A is a square matrix of order 2 with trace equal to 5 and determinant equal to 6, then the sum of...

A square matrix A is nilpotent if some positive integer power of A equals the zero matrix; the deter...

Applying the property that adding a multiple of one row to another leaves a determinant unchanged, t...