Compute the following:\left[ \begin{array}{cc}{a} & {b} \\ {-b} & {a}\end{array}\right]+\left[ \begin{array}{ll}{a} & {b} \\ {b} & {a}\end{array}\right]\left[ \begin{array}{rrr}{-1} & {4} & {-6} \\ {8} & {5} & {16} \\ {2} & {8} & {5}\end{array}\right]+\left[ \begin{array}{rrr}{12} & {7} & {6} \\ {8} & {0} & {5} \\ {3} & {2} & {4}\end{array}\right]\left[ \begin{array}{cc}{a^{2}+b^{2}} & {b^{2}+c^{2}} \\ {a^{2}+c^{2}} & {a^{2}+b^{2}}\end{array}\right]+\left[ \begin{array}{cc}{2 a b} & {2 b c} \\ {-2 a c} & {-2 a b}\end{array}\right]\left[ \begin{array}{cc}{\cos ^{2} x} & {\sin ^{2} x} \\ {\sin ^{2} x} & {\cos ^{2} x}\end{array}\right]+\left[ \begin{array}{cc}{\sin ^{2} x} & {\cos ^{2} x} \\ {\cos ^{2} x} & {\sin ^{2} x}\end{array}\right]

Compute the following:\left[ \begin{array}{cc}{a} & {b} \\ {-b} & {a}\

1.	Compute the following:\left[ \begin{array}{cc}{a} & {b} \\ {-b} & {a}\end{array}\right]+\left[ \begin{array}{ll}{a} & {b} \\ {b} & {a}\end{array}\right]\left[ \begin{array}{rrr}{-1} & {4} & {-6} \\ {8} & {5} & {16} \\ {2} & {8} & {5}\end{array}\right]+\left[ \begin{array}{rrr}{12} & {7} & {6} \\ {8} & {0} & {5} \\ {3} & {2} & {4}\end{array}\right]\left[ \begin{array}{cc}{a^{2}+b^{2}} & {b^{2}+c^{2}} \\ {a^{2}+c^{2}} & {a^{2}+b^{2}}\end{array}\right]+\left[ \begin{array}{cc}{2 a b} & {2 b c} \\ {-2 a c} & {-2 a b}\end{array}\right]\left[ \begin{array}{cc}{\cos ^{2} x} & {\sin ^{2} x} \\ {\sin ^{2} x} & {\cos ^{2} x}\end{array}\right]+\left[ \begin{array}{cc}{\sin ^{2} x} & {\cos ^{2} x} \\ {\cos ^{2} x} & {\sin ^{2} x}\end{array}\right]
Answer» i)a+a b+b = 2a 2b -b+b a+a 0 2aii) a^2+2ab+b^2 b^2+2bc+c^2 a^2-2ac+c^2 a^2-2ab+b^2=(a+b)^2 (b+c)^2 (a-c)^2 (a-b)^2iii) 11 11 0 16 5 21 5 10 9iv) sin^2x+cos^2x sin^2x+cos^2x= 1 1 sin^2x+cos^2x sin^2x+cos^2x 1 1