Question

What is an inverse in matrix?

Answer 1

Inverse matrix:

• An inverse matrix is a matrix that when multiplied with a given matrix gives the identity matrix.
• Mathematically this can be written as ${\mathbf{A}}^{\mathbf{-}\mathbf{1}}\mathbf{A}\mathbf{=}\mathbf{I}$,where $A$is an square matrix.
• The equation of an inverse matrix is ${\mathbf{A}}^{\mathbf{-}\mathbf{1}}\mathbf{=}\frac{\mathbf{1}}{\left|A\right|}\mathbf{adj}\mathbf{}\mathbf{A}$
• If the determinant $\left|A\right|=0$, then the inverse matrix does not exist.
• Inverse matrices exist only for non-singular matrices.