In determinants matrix A and its inverse is A^-1, then A = 1/(A^-1)?

 

What are natural magnets and why do they have magnetic properties?

 Natural magnets are permanent magnets found in the earth's crust, such as lodestone (a magnetized form of the iron oxide mineral magnetite). They form naturally when deposits are exposed to intense magnetic fields—like the Earth's magnetic field over long periods or powerful natural events like lightning strikes. 

Why They Have Magnetic Properties

Electron Spin: Every atom has electrons that spin and create tiny magnetic fields.
Unpaired Electrons: In most materials, these magnetic fields cancel each other out. In magnetic materials like iron, many electrons point in the same direction.
Magnetic Domains: Atoms group into tiny regions called domains.
Alignment: In a natural magnet, these domains point in one uniform direction, creating a strong overall magnetic force.

Electrons drift in a conductor from lower to higher potential, does this mean that all free electrons are moving in the same direction?

 

find value of a for which f(x) = x^2 -2ax + b f(x) is an increasing function for x>0

 

Determinant of a skew symmetric matrix

 

If A is a square matrix of order 3 such that det(A)=9, then det(9A^-1) is?

 

If A is a 3x3 matrix , B is a 3x1 matric and C is a 1x3 matric then only AB and BC are defined?

 The statement is false because, in addition to AB and BC, the matrix products AC and  CB are also perfectly well-defined. 

Conclusion

Apart from AB and BC, the products CB and CA are also defined.