Let A is a non-singular matrix such that A2 -I- Then the inverse of A2 will be where I - identity matrix

A^2 = I ⇒ A =A^ 1 Also (kA)^ 1=1kA^ 1 Hence, (12A )^ 1= 2 A^ 1=2A ...

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Finding Integral Part of Numbers of the Form a^b Where a Is Irrational

Let A is a no...

Question

Let $A$ is a non-singular matrix such that $A^{2} = I .$ Then the inverse of $\frac{A}{2}$ will be (where $I =$ identity matrix)

2 A

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\frac{A^{- 1}}{2}

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\frac{A}{2}

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A^{2}

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Solution

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A^{2} = 2 A - I

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A^{2} - A + 2 I = 0

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