###### Asked in Math and ArithmeticAlgebra

Math and Arithmetic

Algebra

# Is Inverse of the inverse matrix the original matrix?

## Answer

###### Wiki User

###### May 31, 2009 4:49PM

Let A by an nxn non-singular matrix, then A-1 is the inverse of A. Now

(A-1 )-1 =A

So the answer is yes.

## Related Questions

###### Asked in Math and Arithmetic, Algebra, Linear Algebra

### What is inverse of 2x2 matrix A can you find the inverse of any given matrix?

The inverse of a 2x2 matrix:
[a b]
[c d]
is given by
__1___[d -b]
ad - bc [-c a]
ad - bc is the determinant of the matrix; if this is 0 the
matrix has no inverse.
The inverse of a 2x2 matrix is also a 2x2 matrix.
The browser used here is not really suitable to give details of
the inverse of a general matrix.
Non-singular square matrices have inverses and they can always
be found. Singular, or non-square matrices do not have a proper
inverses but canonical inverses for these do exist.

###### Asked in Algebra, Linear Algebra

### What is an orthogonal matrix?

A matrix A is orthogonal if itstranspose is equal to it inverse.
So
AT is the transpose of A and A-1 is the inverse.
We have AT=A-1
So we have :
AAT= I, the identity matrix
Since it is MUCH easier to find a transpose than an inverse,
these matrices are easy to compute with. Furthermore, rotation
matrices are orthogonal.
The inverse of an orthogonal matrix is also orthogonal which can
be easily proved directly from the definition.

###### Asked in Linear Algebra, How To

### How to find the Inverse of a square symmetric matrix?

You can factorize the matrix using LU or LDLT factorization
algorithm. inverse of a diagonal matrix (D) is really simple. To
find the inverse of L, which is a lower triangular matrix, you can
find the answer in this link.
www.mcs.csueastbay.edu/~malek/TeX/Triangle.pdf
Since (A T )-1 = (A-1 )T for all matrix, you'll just have to
find inverse of L and D.

###### Asked in Math and Arithmetic

### What is the inverse matrix used for?

The inverse of a matrix is used for many different statistics.
While you can add, subtract, or multiply matrices, you cannot
divide them. However, if you multiple by the inverse of a matrix,
this is equivalent to dividing. For example, if you divide 6 by 3
you get 2; however, you could also multiply 6 by the inverse of 3,
1/3, and get the same answer.

###### Asked in Math and Arithmetic

### How do find matrix inverse of 4cross 4matrix?

Next to your 4x4 matrix, place the 4x4 identity matrix on the
right and adjoined to the one you want to invert. Now you can use
row operations and change your original matrix on the left to a 4x4
identity matrix. Each time you do a row operation, make sure you do
the same thing to the rows of the original identity matrix. You end
up with the identity now on the left and the inverse on the right.
You can also calculate the inverse using the adjoint. The adjoint
matrix is computed by taking the transpose of a matrix where each
element is cofactor of the corresponding element in the original
matrix. You find the cofactor t of the matrix created by taking the
original matrix and removing the row and column for the element you
are calculating the cofactor of. The signs of the cofactors
alternate, just as when computing the determinant