First slide

Transpose of matrix

Question

The number of values of $λ$ for which there exist a non-zero 3x3 matrix A such that $A^{'} = λ A$ is :

Moderate

A

0
B

1
C

2
D

infinite

Solution

We have
$A = {(A^{'})}^{'} = (λ A)^{'} = λ A^{'} = λ^{2} A$ .
As $A \neq 0, λ^{2} = 1 \Rightarrow λ = \pm 1$ .
For $λ = 1$ all non-zero symmetric matrices can work as A.
For $λ = - 1$ , all non-zero skew symmetric matrices can work as A.

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