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Question

Let M be the set of all 2×2 matrices with entries from the set of real numbers R. Then the function f:MR defined by f(A)=|A| for every AM, is

A
One-one and onto
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B
Neither one-one nor onto
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C
One-one but not onto
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D
Onto but not one-one
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Solution

The correct option is D Onto but not one-one
f:MR defined by f(A)=|A| for every AM
The function is the determinant of the matrix
We know that, two different matrices can have a same determinant
For example, A=[1011] and B=[2111]
Then |A|=1=|B|, but AB
So, the function will not be one-one.
Now, determinants can have any real values, so range of the function will be R.
Thus, the function will be onto.
Hence, option D is correct

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