Invertible matrix: Invertible matrices are defined as

Invertible matrices are defined as the matrix whose inverse exists. We define a matrix as the arrangement of data in rows and columns, if any matrix has m rows and n columns then the order of the matrix is m × n where m and n represent the number of rows and columns respectively. We ended the previous section by stating that invertible matrices are important. Since they are, in this section we study invertible matrices in two ways. First, we look at ways to tell whether or not a matrix is invertible, and second, we study properties of invertible matrices (that is, how they interact with other matrix operations). Inverse matrix An n × n matrix, A, is invertible if there exists an n × n matrix, A -1, called the inverse of A, such that A -1 A = AA -1 = I n where I n is the n × n identity matrix. We will denote the identity matrix simply as I from now on since it will be clear what size I should be in the context of each problem. Remember that I is special because for any other matrix A, IA = AI = A Note that given an n × n invertible matrix, A, the following conditions are equivalent (they are ... Today we investigate the idea of the ”reciprocal” of a matrix. For reasons that will become clear, we will think about this way: The reciprocal of any nonzero number \ (r\) is its multiplicative inverse. That is, \ (1/r = r^ {-1}\) such that \ (r \cdot r^ {-1} = 1.\) This gives a way to define what is called the inverse of a matrix. First, we have to recognize that this inverse does not exist for all matrices. It only exists for square matrices And not even for all square matrices ...