If A=1 23 4, then A2−5A−I equals

A2=1 23 41 23 4=7101522We haveA2−5A=7101522−51 23 4=2 00 2=2I⇒A2−5A−I=I

If A=1 23 4, then A2−5A−I equals

A2=1 23 41 23 4=7101522We haveA2−5A=7101522−51 23 4=2 00 2=2I⇒A2−5A−I=I

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If $A = [\begin{array}{ll} 1 2 \\ 3 4 \end{array}]$ , then $A^{2} - 5 A - I$ equals

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$A^{2} = [\begin{array}{ll} 1 2 \\ 3 4 \end{array}] [\begin{array}{ll} 1 2 \\ 3 4 \end{array}] = [\begin{array}{cc} 7 & 10 \\ 15 & 22 \end{array}]$

We have

$A^{2} - 5 A = [\begin{array}{cc} 7 & 10 \\ 15 & 22 \end{array}] - 5 [\begin{array}{ll} 1 2 \\ 3 4 \end{array}] = [\begin{array}{ll} 2 0 \\ 0 2 \end{array}] = 2 I$

$\Rightarrow A^{2} - 5 A - I = I$

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If $A = [\begin{array}{ll} 1 2 \\ 3 4 \end{array}]$ , then $A^{2} - 5 A - I$ equals