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If, for an n*n matrix, A, there exists a matrix B such that AB = I, where I is the n*n identity matrix, then the matrix B is said to be the inverse of A. In that case, BA = I (in general, with matrices, AB ≠BA)
I is an n*n matrix consisting of 1 on the principal diagonal and 0s elsewhere.
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When is it important for a matrix to be square?
In the context of matrix algebra there are more operations that one can perform on a square matrix. For example you can talk about the inverse of a square matrix (or at least some square matrices) but not for non-square matrices.
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.
What is the mutiplicative inverse?
The multiplicative inverse of any non-zero number x, is the number y such that x*y = 1 = y*x. y may also be written as 1/x. Multiplicative inverses also exist for non-singular matrices.
What is the condition for the addition of matrices?
The matrices must have the same dimensions.
Do all matrices have determinant?
Only square matrices have a determinant
