Matrix

Question

If

$A=\begin{bmatrix} 1 &2 &2 \\ 2&1 &-2 \\ a&2 &b \end{bmatrix}$

then$AAA^{T}=3I$

$I$ is a $3\times 3$ identity matrix

$\left (a,b \right )$ can be ____________

Comments

(-6 , -1/2) ?

Answer 1

you can solve by using some rules

AAAt=3I

A I=3I   (AAt=I)  ORTHOGONAL MATRIX by solving you get the answer a=0,b=3

Comments

Answer should be a= -2 and b = -1.

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How you know it is orthogonal matrix ?