A square matrix $A$ is said to be an idempotent matrix if $A^2=A$. If $A$ is a non-singular idempotent matrix, then

Q. A square matrix $A$ is said to be an idempotent matrix if $A^2=A$. If $A,B$ and $A+B$ are idempotent matrices, then

Q. A square matrix $A$ is said to be an idempotent matrix if $A^2=A$ and $B=I-A$, then

Q. A square matrix $A$ is said to be an idempotent matrix if $A^2=A$. If $A$ and $B$ are idempotent matrices and $AB=BA$, then which of the following is an idempotent matrix

Q. Let matrix $A$ be an idempotent matrix and $B$ be a matrix such that $A+B=l.$
Statement-1 : B is an idempotent matrix. and
Statement-2 : $AB=BA=0.$

Q. Observe the following lists :
List - I List - II
A) If A is a singular 1) ${\left(detA\right)}^{n-1}$
matrix then adj A is
B) If A is a square 2) an idempotent Matrix
matrix then detA=
C) If $A^2$=A then A is 3) Singular
D) If A is square matrix 4) $det{A}^T$
of type n then det (adj A) = 5) a nil potent matrix
The correct match for list - I from list - II is