Final answer:
To find matrix A given that its inverse is [2 1, 4 1], one has to compute a matrix that when multiplied by this inverse yields the identity matrix. This process involves solving systems of equations or computational methods.
Step-by-step explanation:
The question concerns finding matrix A given its inverse. If A is a nonsingular matrix with an inverse [2 1, 4 1], we can find matrix A by using the property that when a matrix is multiplied by its inverse, the result is the identity matrix. Therefore, for matrix A and its inverse A-1, the following equation holds true: AA-1 = I where I is the identity matrix.
Here, A-1 is given as:
[2 1]
[4 1]
To find A, we need to compute a matrix that when multiplied by A-1 results in:
[1 0]
[0 1]
This can be solved by executing the matrix multiplication of A-1 with the identity matrix and equating it to A. However, keep in mind that solving this involves systems of equations or computational methods, which go beyond this example.