The number of solutions of the matrix equation A 2- lbeginbmatrix 1 - 0 0 - 1 lendbmatrix isA- 2B- 4C- 8D- infinitely many

The correct option is D infinitely many A= ± I, ±[ 1 amp;0; c amp; 1 ], [ a amp;b; 1 a^2/b amp; a ] where a, b, c are arbitrary and b ≠ 0 ...

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Standard XII

Mathematics

Symmetric Matrix

The number of...

Question

The number of solutions of the matrix equation $A^{2}$ = $[\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ is

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infinitely many

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Solution

The correct option is D
infinitely many

$A = \pm I, \pm [\begin{matrix} 1 & 0 c & - 1 \end{matrix}], [\begin{matrix} a & b \frac{1 - a^{2}}{b} & - a \end{matrix}]$

where a, b, c are arbitrary and $b \neq 0$

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The correct option is D infinitely many A=±I, ±[10c−1], [ab1−a2b−a] where a, b, c are arbitrary and b≠0

The number of solutions of the matrix equation $A^{2}$ = $[\begin{matrix} 1 & 0 0 & 1 \end{matrix}]$ is

The correct option is D
infinitely many

$A = \pm I, \pm [\begin{matrix} 1 & 0 c & - 1 \end{matrix}], [\begin{matrix} a & b \frac{1 - a^{2}}{b} & - a \end{matrix}]$

where a, b, c are arbitrary and $b \neq 0$