If the matrix A = 2 5 1 3 , then the value of A 100 + A 98 A 20 + A 18 is equal to

Question: Answered & Verified by Expert

If the matrix

A = [\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}]

, then the value of

\frac{|A^{100} + A^{98}|}{|A^{20} + A^{18}|}

is equal to

MathematicsDeterminantsJEE Main

Options:

Solution:

1413 Upvotes Verified Answer

The correct answer is:

1

|A| = |\begin{matrix} 2 & 5 \\ 1 & 3 \end{matrix}| = 6 - 5 = 1

\frac{|A^{100} + A^{98}|}{|A^{20} + A^{18}|} = \frac{|A^{98}| |A^{2} + I|}{|A^{18}| |A^{2} + I|} = {|A|}^{80} = 1

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