what is the inverse of a matrix?

Answer 1

The inverse of a matrix
The inverse of a square n × n matrix A, is another n × n matrix denoted by A−1 such that
AA−1 = A−1A = I

for a more detailed answer check out

Answer 2

its the matrix times by "to the power of" -1

so to work it out you take I of whatever matrix you want to use so for a 3 x 3 matrix you would use

1 0 0
0 1 0
0 0 1

you put this next to the matrix

for example the inverse of matrix

2 4
1 3

it equals
2 4 1 0
1 3 0 1

2 4 1 0
0 -2 1 -2

2 0 3 -4
0 -2 1 -2

1 0 3/2 -2
0 1 -1/2 1

therefore that matrix to the power of -1

3/2 -2
-1/2 1

sorry i couldn't use the brackets and show all working but if you have problems with that just tell me and i can help out

Answer 3

For a matrix of a linear operator, it is the matrix of the inverse linear operator. If the operator is not invertible, so is the matrix.
E.g. if a matrix denotes some clockwise rotation, then its inverse would be a matrix of counter-clockwise rotation by the same angle. If it denotes 2x uniform scale, then its inverse will be a matrix of 1/2x uniform scale. Etc.
Just like the composition of an operator and its inverse gives identity operator, the product of the matrix and its inverse will be an identity matrix.
Inverting a matrix is basically the same as solving a linear equation system.
Look up the details (and the methods of matrix inversion) here:
http://en.wikipedia.org/wiki/Invertible_matrix

Answer 4

The inverse of a square matrix is another matrix of equal order with the special property that the two matrices, when multiplied (in either order), give an identity matrix as their product.

If A and B are square matrices, and AB = BA = I, then A and B are inverses of each other.

Answer 5

Any matrix A when multiplied by any other matrix B having same order such that,
A*B=I
where I is an identity matrix of the same order then such a matrix B is called inverse of matrix A.
Generally inverse of A is represented as A^-1 i.e B=A^-1

Answer 6

Assuming we have a square matrix A, which is non-singular ( i.e. det(A) does not equal zero ), then there exists an nxn matrix A-1 which is called the inverse of A, such that this property holds:

AA-1= A-1A = I where I is the identity matrix.
The inverse of a 2x2 matrix

AX = C
A–1AX = A–1C
IX = A–1C
X = A–1C

Answer 7

Let the matrix be M, and the inverse of this matrix would be M-1, where:

(M) (M-1) = identity matrix

Answer 8

1 0 0 0 ... 0
0 1 0 0 ... 0
. . . .
0 0 0 0 ... 1 (nxn) the unit matrix. If AxA'=I then A' is inverse of A

But A is a square matrix

Answer 9

the inverse of a matrix is a matrix if multiplied to the left side of the matrix, it will result in the identity matrix. the reason for this is because in simple algebra, in order to solve for Ax=b, you would need to divide both sides by A to solve for x. but in the world of matrices, you cannot divide matrices. you can only multiply or add/substract. the matrix that is multiplied onto A to result in the identity matrix is the inverse of A. represent in this form A^(-1)

hence you will have Ax=b, solve for x

A^(-1)*Ax=A^(-1)b
x=A^(-1)b

also, A matrix is invertible if and only if its determinant is nonzero.


here's a good source to look at...

http://en.wikipedia.org/wiki/Invertible_matrix

Answer 10

The inverse of the matrix is xirtam.