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Definition of a Determinant

If A is a s...

Question

If $A$ is a square matrix such that $A^{2} = A$ , then $| A |$ equals

0

1

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- 2

2

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- 3

3

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None of these

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Solution

The correct option is B $0$ or $1$
Since, $A$ is a square matrix.
Given, $A^{2} = A$
Taking determinant on both sides. we get,
$\Rightarrow | A^{2} | = | A |$
$\Rightarrow | A^{2} | - | A | = 0$
$\Rightarrow | A | (| A | - 1) = 0$
$\Rightarrow | A | = 0$ or $| A | - 1 = 0$
$\Rightarrow | A | = 0$ or $| A | = 1$
Option $A$ is correct.

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