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Question

# Choose the correct statement or statements :

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

## The correct options are B every identity matrix is a scalar matrix C transpose of transpose of a matrix gives the matrix itselfA 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.∴ Every Identity matrix is a scalar matrix.(AT)T=A∴ 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|≠0i.e iff A is invertible.Hence, options B and C.

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