Final answer:
To find an elementary matrix E such that EA = B, we can multiply both sides of the equation by the inverse of matrix A, obtaining E = BA^{-1}.
Step-by-step explanation:
An elementary matrix is a matrix that can be obtained from the identity matrix by performing a single elementary row operation. To find an elementary matrix E such that EA = B, we can perform the inverse operation on matrix A to eliminate the need for row operations. The inverse of a matrix A is denoted by A-1, and it has the property that AA-1 = I, where I is the identity matrix.so, to find E, we can multiply both sides of the equation EA = B by A-1, giving us EAA-1 = BA-1. Since AA-1 = I, the equation becomes EI = BA-1. Therefore, the elementary matrix E that satisfies EA = B is E = BA-1.