SOLUTION: What is an invertible matrix and how do you show that it is invertible?

Question 1044869: What is an invertible matrix and how do you show that it is invertible?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
A square matrix

is invertible if there exists a matrix

such that

where I is the identity matrix.

A matrix is invertible if and only if its determinant is not zero.
RELATED QUESTIONS
How does one show that an operator is... (answered by stanbon)

Which 1x1 matrix is... (answered by ikleyn)

suppose A is a 2 x 2 matrix as follows A = [56 34] how do i decide whether A (answered by Fombitz)

a square matrix A is said to be idempotent A^2=A (a)give an example of idempotent... (answered by Edwin McCravy)

If A is an invertible 2 x 2 matrix,then A^t is invertible and (At)^-1 = (A^-1)^t. (answered by jim_thompson5910)

Show that the system of linear equation AX = B has a unique solution if and only if the... (answered by rothauserc)

A is a 2x3 matrix and B a 3x2 matrix is A-B defined A is invertible 3x3 matrix B is... (answered by stanbon,jim_thompson5910)

Some functions that aren't invertible can be made invertible by restricting their... (answered by stanbon)

A square matrix A is idempotent if A^2 = A. a) Show that if A is idempotent, then... (answered by kev82)