![]() ![]() In the next article, we will discuss about how to find the solution to a system of linear equations using determinant method popularly known as Cramer’s rule. Readers must check the correctness of the inverse as an exercise. We can compute the inverse of matrix using determinant and the adjoint matrix. Let us find the determinant of the matrix by multiplying first row of matrix A and first row of cofact matrix of A. In the previous example, we computed the adjoint matrix of A which is If the determinant of a square matrix is nonzero, then the following will give inverse matrix of a matrix The only condition is that the determinant must not be zero. The adjoint matrix can also be used to find the inverse of a matrix. Step4: Finally, transpose the cofactor matrix to get the adjoint of matrix Inverse Matrix Using Adjoint Assign negative or positive sign to minors based on following pattern. Step3: Given the matrix of minors we can quickly find the cofactor matrix by shortcut method. ![]() Step2: We must find the matrix of minors for Step1: The given matrix is a square matrix. Solution: We will find solution to this matrix in a step-by-step manner.
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