# Algebra Examples

Combine the similar matrices with each others.

Combine the same size matrices and by adding the corresponding elements of each.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

Simplify element of the matrix.

The inverse of a matrix can be found using the formula where is the determinant of .

If then

These are both valid notations for the determinant of a matrix.

The determinant of a matrix can be found using the formula .

Simplify the determinant.

Simplify each term.

Multiply by to get .

Multiply by to get .

Subtract from to get .

Substitute the known values into the formula for the inverse of a matrix.

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Multiply by each element of the matrix.

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .

Simplify element by multiplying to get .