An inverse matrix is like a number puzzle. In the puzzle, you start with a row of numbers like 5, 7, and 8. To solve the puzzle, you switch the numbers around so the row looks like 8, 5, and 7. An inverse matrix does the same thing but for matrices (matrices are like tables of numbers).

For example, imagine you start with a 2x2 matrix that looks like this:

Matrix A = | 5 8 |

| 2 4 |

To solve this matrix, you have to come up with another matrix that when you multiply it times Matrix A it produces the Identity Matrix. This Identity Matrix is a 2x2 matrix with 1 in the top left and 0 everywhere else.

Matrix A times Matrix B should look like this:

| 5 8 | | x y | = | 1 0 |

| 2 4 | | u v | | 0 1 |

So now you have to figure out what x, y, u, and v are.

This can be done by multiplying Matrix A by Matrix B and then solving for each of the variables.

Matrix B will be the inverse matrix for Matrix A.

The answer for Matrix B should look like this:

Matrix B = | 9 -8 |

|-2 4 |

So if you take Matrix A and multiply it times Matrix B, you will get the Identity Matrix.

Hope that helps! :)

For example, imagine you start with a 2x2 matrix that looks like this:

Matrix A = | 5 8 |

| 2 4 |

To solve this matrix, you have to come up with another matrix that when you multiply it times Matrix A it produces the Identity Matrix. This Identity Matrix is a 2x2 matrix with 1 in the top left and 0 everywhere else.

Matrix A times Matrix B should look like this:

| 5 8 | | x y | = | 1 0 |

| 2 4 | | u v | | 0 1 |

So now you have to figure out what x, y, u, and v are.

This can be done by multiplying Matrix A by Matrix B and then solving for each of the variables.

Matrix B will be the inverse matrix for Matrix A.

The answer for Matrix B should look like this:

Matrix B = | 9 -8 |

|-2 4 |

So if you take Matrix A and multiply it times Matrix B, you will get the Identity Matrix.

Hope that helps! :)