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The inverse of a non-singular, n*n matrix, A Is another n*n matrix, A' such that A*A' = A'*A =I(n), the n*n identity matrix.

Singular square matrices do not have inverses, nor do non-square matrices.

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Related Questions

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.


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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.


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If an identity matrix is the answer to a problem under matrix multiplication, then each of the two matrices is an inverse matrix of the other.


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No. A square matrix has an inverse if and only if its determinant is nonzero.


Define inverse of matrix?

From Wolfram MathWorld: The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A-1 such that AA-1=I where I is the identity matrix.


What are the applications of det of a matrix?

it is used to find the inverse of the matrix. inverse(A)= (adj A)/ mod det A


How do you find a variable in a matrix if there is no inverse?

The fact that the matrix does not have an inverse does not necessarily mean that none of the variables can be found.


How do you call a matrix that if you multiplied it by the original matrix you would get the identity matrix?

That is called an inverse matrix


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Inverse of 2x1 matrix?

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How to find the Inverse of a square symmetric matrix?

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