First slide

Operations of matrix

Question

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

Easy

A

O
B

I
C

2I
D

none of these

Solution

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