Transpose Of Matrices

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A matrix A is both symmetric and skew symmetric if A is

• Null matrix

• unit matrix

• row matrix

• none of these

(A')'=

• -A'

• -A

• A

• A'

(kA)'= (where k is any scalar)

• -kA

• kA'

• $\frac{1}{k}A'$

• -kA'

(-A)'=

• A'

• -A'

• $\left(A'\right)^{-1}$

• -a

(A+B)'=

• A'-B'

• A+B

• B'-A'

• A'+B'

(AB)'=

• A'B'

• B'A'

• $\frac{1}{A'B'}$

• BA

A square matrix is known as symmetric matrix if

• A+A'=0

• A=A'

• $A-A'\ne0$

• None of these

Square matrix B is known as skew symmetric if

• B=B'

• B'+B=0

• B-B'=0

• none of these

Every square matrix can be uniquely expressed as sum of a symmetric and skew symmetric matrix.

• True

• False