First slide

Operations of matrix

Question

If $A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & - 1 \end{matrix}]$ then $A^{2}$ is equal to

Moderate

A

a null matrix
B

a unit matrix
C

$- A$
D

$A$

Solution

We have
$A^{2} = [\begin{array}{rrr} 1 0 0 \\ 0 1 0 \\ a b - 1 \end{array}] [\begin{array}{rrr} 1 0 0 \\ 0 1 0 \\ a b - 1 \end{array}] = [\begin{array}{rrr} 1 0 0 \\ 0 1 0 \\ 0 0 1 \end{array}] = a$ unit matrix.

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