Q:
# What Is the Inverse of a 2x2 Matrix?

**The inverse of a two-by-two matrix is another two-by-two matrix that, when multiplied by the original matrix, gives the identity matrix.** Gauss-Jordan elimination and LU decomposition are two methods that can be employed to identify the inverse of a matrix.

A two-by-two matrix has two rows and two columns, with values a and b in the first row and c and d in the second row. Make a new matrix and place the values of d and negative b in the first row, then place the values of negative c and a in the second row. Multiply this new matrix by the value of 1 over the determinant, which is 1 over the quantity a times d minus b times c. The final result of this series of computations is the inverse of the original matrix.

Using software such as Mathematica simplifies the tedious process of calculating the inverse of a matrix, while also reducing the chance of making a computation error.

Learn more about Algebra-
Q:
## What Do You Call Two Numbers Whose Product Is One?

A: A number when multiplied by its multiplicative inverse, or its reciprocal, yields a product of one, which is known as the multiplicative identity of a numb... Full Answer >Filed Under: -
Q:
## What Is a Unitary Matrix?

A: A unitary matrix is a matrix that when multiplied by its complex conjugate transpose matrix, equals the identity matrix. This implies that the complex conj... Full Answer >Filed Under: -
Q:
## What Is a Matrix Inverse?

A: When a matrix is multiplied by its inverse, the resulting product is the identity matrix. Thus, the inverse of a matrix can be found by dividing the identi... Full Answer >Filed Under: -
Q:
## What Is the Equation for Inverse Variation?

A: The general formula for inverse variation is k equals y times x, where k is a constant quantity, y is one variable and x is another variable. Under inverse... Full Answer >Filed Under: