# 3x3 Matrix Transpose, Inverse, Trace, Determinant and Rank

3x3 Matrix Transpose, Inverse, Trace, Determinant and Rank

The transpose of a matrix is a matrix whose rows and columns are reversed.

A

A

The inverse of a matrix is a matrix such that and A equal the identity matrix. If the inverse exists, the matrix is said to be nonsingular.

3×3

A

-1

A

A

-1

A

-1

A

The trace of a matrix is the sum of the entries on the main diagonal (upper left to lower right).

The determinant is computed from all the entries of the matrix. The matrix is nonsingular if and only if . In that case, the equation has a unique solution.

Δ

A

Δ≠0

Ax=b

The matrix rank is the number of linearly independent columns and is equal to three when the matrix is nonsingular.