Q.Matrices $A$ and $B$ are invertible of each other iff

Two square matrices are inverses of each other exactly when both products give the identity matrix.

By definition, if $A$ and $B$ are square matrices of the same order such that $AB=BA=I$ (the identity matrix), then $B$ is called the inverse of $A$ (written $B=A^{-1}$) and $A$ is the inverse of $B$. A si …

A matrix has no inverse exactly when its determinant is zero.

A square matrix is invertible only if it is non-singular, i.e. $\det\ne 0$. "No inverse matrix" means the matrix IS singular, so we need $\det = 0$.

…

By definition, A and B are inverses of each other exactly when their product (in either order) gives the identity matrix.

A square matrix $B$ is the inverse of $A$ if $AB=BA=I$, where $I$ is the identity matrix of the same order. This is the standard definition of ma …

Inverse of a matrix is defined by the identity relation on both sides.

By definition, if $A$ is a square matrix and there exists a matrix $B$ of the same order such that $AB=BA=I$ (the identity matrix), then $B$ is called the inverse of $A$ (written $B=A^{-1}$), and $A$ is the i …