What is the condition for a matrix to be invertible?
Answer (1)
Condition for a Matrix to Be Invertible
A square matrix is invertible (also called non-singular) if there exists another matrix, called its inverse, such that A
-1
A=A A
-1
=I, where I is the identity matrix of the same order.
The key condition for a matrix to be invertible is that its determinant must not be zero, i.e., {det}(A) not equal to 0.
If {det}(A)=0, the matrix is called singular and does not have an inverse.
Invertible matrices are essential in solving systems of linear equations, finding matrix equations, and various applications in linear algebra.
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