Determinant of invertible matrix

The determinant of the inverse of an invertible matrix is the inverse of the determinant: det(A^-1) = 1 / det(A) [6.2.

1. Is determinant of matrix invertible zero?
2. What is the determinant of a 3x3 invertible matrix?
3. Are all matrices with non-zero determinant invertible?
4. Can invertible matrix have negative determinant?

Is determinant of matrix invertible zero?

If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses. Find the inverse of the matrix A = ( 3 1 4 2 ).

What is the determinant of a 3x3 invertible matrix?

To find the determinant of a 3x3 matrix, find the sum of the product of the elements of any of its row/column and their corresponding cofactors. Here is an example. A = ⎡⎢⎣12−1212−121⎤⎥⎦ [ 1 2 − 1 2 1 2 − 1 2 1 ] .

Are all matrices with non-zero determinant invertible?

Theorem 2: A square matrix is invertible if and only if its determinant is non-zero.

Can invertible matrix have negative determinant?

Hence, the determinate of the matrix can be negative.