Question

Choose the correct statement or statements :

• A. every scalar matrix is an identity matrix
• B. every identity matrix is a scalar matrix
• C. transpose of transpose of a matrix gives the matrix itself
• D. for every square matrix A there exists another matrix B such that AB = I = BA.

Answer 1

Answer: (B), (C)

The correct options are
B every identity matrix is a scalar matrix
C transpose of transpose of a matrix gives the matrix itself

A scalar matrix is a square matrix in which all diagonal elements are equal and non-diagonal elements are zero.
An Identity matrix is a scalar matrix in which diagonal elements are $1$.
$\therefore$ Every Identity matrix is a scalar matrix.
$(A^T{)}^T=A$
$\therefore$ Transpose of transpose of a matrix gives the matrix itself.
for every square matrix A there exists another matrix B such that $AB=I=BA$.
iff $|A|\ne 0$
i.e iff $A$ is invertible.
Hence, options B and C.