Question

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Answer 1

Answer :-

$\left[\begin{array}{ccc}4&9\\5&7\\\end{array}\right]$ is the matrix.

Step-by-step explanation :-

Given :

A = $\left[\begin{array}{ccc}1&0\\2&1\end{array}\right]$ and B = $\left[\begin{array}{ccc}2&3\\-1&0\end{array}\right]$.

To find :

A² + AB + B².

Solution :

A² :-

$\left[\begin{array}{ccc}1&0\\2&1\end{array}\right]$  $\times$ $\left[\begin{array}{ccc}1&0\\2&1\end{array}\right]$

∴,

(1×1) + (0×2) (1×0) + (0×1)

(2×1) + (1×2) (2×0) + (1×1)

$\left[\begin{array}{ccc}1&0\\4&1\end{array}\right]$ = A²

B² :-

$\left[\begin{array}{ccc}2&3\\-1&0\end{array}\right]$  $\times$  $\left[\begin{array}{ccc}2&3\\-1&0\end{array}\right]$

∴,

(2×1) + (3×-1) (2×3) + (3×0)

(-1×2) + (0×-1) (-1×3) + (0×0)

$\left[\begin{array}{ccc}1&6\\-2&0\\\end{array}\right]$ = B²

AB :-

$\left[\begin{array}{ccc}1&0\\2&1\end{array}\right]$  $\times$  $\left[\begin{array}{ccc}2&3\\-1&0\end{array}\right]$

(1×2) + (0×-1) (1×3) + (0×0)

(2×2) + (1×-1) (2×3) + (1×0)

$\left[\begin{array}{ccc}2&3\\3&6\end{array}\right]$ = AB

A² + AB + B² :-

$\left[\begin{array}{ccc}1&0\\4&1\end{array}\right]$ + $\left[\begin{array}{ccc}2&3\\3&6\end{array}\right]$ + $\left[\begin{array}{ccc}1&6\\-2&0\\\end{array}\right]$

(1+2+1) (0+3+6)

(4+3+-2) (1+6+0)

$\left[\begin{array}{ccc}4&9\\5&7\\\end{array}\right]$ = A² + AB + B²