❖ In this lesson, we have explained how to compute the inverse of a \(4 \times 4\) matrix, which is a precalculus lesson tutorial. The previous lessons showed how to find the inverse of a \(2 \times 2\) and a \(3 \times 3\) matrix.

❖ To find the inverse of a \(4 \times 4\) matrix, you need to write an augmented matrix containing the original matrix and the identity matrix (which has the same size as the original matrix),

Then,

You need to convert the original matrix into the identity matrix using Elementary Row Operations

(Apply Reduced Row Echelon Form (RREF) for the left side of the augmented matrix).

The identity matrix will convert into the inverse of the original matrix as long as you apply the same elementary row operations for the augmented matrix.

❖ Finally, you can confirm or check to see if you have the right answer by

multiplying (the matrix) by (its inverse) and you have to get (the identity matrix).

❖ (The matrix \(A\)) multiplied by (the inverse of the matrix \(A\)) equal to (the identity matrix) of the same size as \(A\),

so, if the inverse of matrix \(A\) exists then

\(A A^{-1} =\) Identity matrix.

❖ Also, we have explained in this lesson that if the inverse of the matrix does not exist (DNE).

Note:

If \(A\) is not a Square Matrix, then the inverse of matrix \(A\) is DNE.

The Square Matrix is a matrix with

the number of rows \(=\) the number of columns.

❖ The number of rows and columns that a matrix has is called its size, order, or dimension.