Question:
For what values of a and b if A = B, where
$A=\left[\begin{array}{cc}a+4 & 3 b \\ 8 & -6\end{array}\right], B=\left[\begin{array}{cc}2 a+2 & b^{2}+2 \\ 8 & b^{2}-5 b\end{array}\right]$
Disclaimer: There is a misprint in the question, $b^{2}-5 b$ should be written instead of $b^{2}-56$.
Solution:
As the given matrices A and B are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get
$a+4=2 a+2 \quad 3 b=b^{2}+2$
$8=8 \quad-6=b^{2}-5 b$
On simplifying, we get
$a=2$ and the common value of $b=2$.
Hence, the values of $a$ and $b$ are 2,2 .