You visited us 1 times! Enjoying our articles? Unlock Full Access!

Algebraic Identities

Find if the g...

Question

Find if the given below operation has identity?

(ii) $a * b = a^{2} + b^{2}$

Open in App

Solution

Given: $a * b = a^{2} + b^{2}$

$e$ is the identity of $$ if

$a e = e * a = a i . e ., a^{2} + e^{2} = e^{2} + a^{2} = a$

There is no possible value of $e$ where,

$a^{2} + e^{2} = e^{2} + a^{2} = a$

So, $*$ has no identity element in $Q .$

Suggest Corrections

Similar questions

If a = 2, b = − 2, find the value of:

(i) a²+ b² (ii) a² + ab + b² (iii) a² − b²

\frac{a}{b}

\frac{(a sinθ - b cosθ)}{(a \sin θ + b cosθ)}

\frac{(a^{2} + b^{2})}{(a^{2} - b^{2})}

\frac{(a^{2} - b^{2})}{(a^{2} + b^{2})}

\frac{a^{2}}{(a^{2} + b^{2})}

\frac{b^{2}}{(a^{2} + b^{2})}

a * b = (a - b)^{2}

a * b = a - b

a * b = a + a b

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program