Step 1: Identify the matrix given in the question. It is a 3x3 matrix with the following values: | 1 0 0 | | 0 1 0 | | 0 0 1 |.
Step 2: Recognize that this matrix is called the identity matrix. The identity matrix has 1s on the diagonal (from the top left to the bottom right) and 0s elsewhere.
Step 3: Understand that the determinant of the identity matrix is always 1, regardless of its size.
Step 4: Conclude that the determinant of the given matrix is 1.
Determinant of a Matrix – The determinant is a scalar value that can be computed from the elements of a square matrix and provides important properties about the matrix, such as whether it is invertible.
Identity Matrix – The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere, and its determinant is always 1.
