Matrices and De...

If A is an invertible matrix of order n, then the determinant of adj (A) is

If A is a non – singular matrix that A³ = A + I, then the inverse of B = A⁶ - A⁵ is

The system of equations -2χ + y + z = a, χ - 2y + z = b and χ + y - 2z = c is constant, if

If the system of linear equations χ + 2y - 3z = 1, (p + 2)z = 3 and (2p + 1)y + z = 2has no solutions, then

If the system of equations aχ + ay - z = 0, bχ - y + bz = 0 and -χ + cy + cz = 0 has a non - trivial solution, then the value of

If B is an invertible matrix and A is a matrix, then

The real value of k for which the system of equations 2kχ - 2y + 3z = 0, χ + ky + 2z = 0 and 2χ + kz = 0, has non - trivial solution is

If the system of homogeneous equations 2χ - 2y + z = 0, χ - 2y + z = 0 and λχ - y + 2z = 0 has infinitely many solutions, then