Yeah, that's more like it.ephemeral1 said:I meant to write AB=BA=I sub n.
OK, now what can you do with that?ephemeral1 said:A^2 - A= 0
What do you mean by that?ephemeral1 said:(a^2)- (a^-1) i=0
I still don't know how you got that or how it relates to A2 - A = 0.ephemeral1 said:(a^2)- (a^-1) i=0
To prove that a matrix A is invertible, you can use the determinant method or the row reduction method. The determinant method involves calculating the determinant of the matrix, while the row reduction method involves performing elementary row operations on the matrix until it is in reduced row echelon form. If the resulting matrix is the identity matrix, then A is invertible.
A matrix is idempotent if it is equal to its own square. In other words, when a matrix A is multiplied by itself, the resulting matrix is A again. This means that A has a special property where repeated multiplication does not change its value.
To prove that a matrix A is idempotent, you can simply multiply A by itself and see if the resulting matrix is equal to A. If it is, then A is idempotent. Alternatively, you can use the definition of idempotency and show that A squared is equal to A.
An idempotent matrix has several important properties that make it useful in linear algebra. For example, it can be used to project vectors onto a subspace, and it is also useful in solving systems of linear equations. Additionally, idempotent matrices have applications in statistics and machine learning.
To prove that an invertible matrix A is idempotent, you can use the fact that A is idempotent if and only if A squared is equal to A. Since A is invertible, you can multiply both sides of the equation A squared = A by A inverse, giving you A = A inverse A. This shows that A is equal to its own inverse, making it idempotent.