If `[[a+b ,2],[ 5 , a b]]=[[6 , 2],[ 5, 8]]`, find the values of `a` and `b`

Consider the matrices A=[[1,-2],[-1,3]] and B=[[a,b],[c,d]] If AB=[[2,9],[5,6]] , find the values of a,b,c,d

If A=[[1 ,-2 , 3],[ -4, 2 ,5]] and B=[[2 , 3],[ 4, 5], [2 , 1]] , then find A B, B A . Show that AB ne BA .

If A=[[8 ,0], [ 4 , -2],[ 3 , 6]] and B=[[2 , -2], [ 4 ,2], [ -5 , 1]] , then find the matrix X , such that 2 A+3 X=5 B .

Consider the matrices A=[[2,-6],[1,2]] and A+3B=[[5,-3],[-2,-1]] Find the transpose of B.

Let A=[[3,6,5],[6,7,8]] and C=[[1,2,-3],[4,5,6]] Find the matrix B such that 2A+B=3C

Let A=[[3 , 7],[ 2, 5]] and B=[[6 , 8],[ 7, 9]] Verify that (A B)^(-1)=B^(-1) A^(-1)

Compute the following: i) [[a, b],[ -b, a]]+[[a, b],[ b , a]] . ii) [[a^2+b^2 , b^2+c^2], [a^2+c^2 , a^2+b^2]]+[[2 a b , 2 b c],[ -2 a c, -2 a b]] iii) [[-1 , 4 ,-6] ,[ 8, 5 , 16],[ 2 , 8 , 5]]+[[12, 7 ,6 ],[ 8, 0, 5],[ 3, 2, 4]] iv) [[cos ^2 x ,. sin ^2 x],[ sin ^2 x , cos ^2 x]]+[[sin ^2 x, cos ^2 x ],[ cos ^2 x ,sin ^2 x]] .

Find A B , if A=[[6, 9],[ 2 , 3]] and B=[[2, 6 ,0 ],[ 7,9,8]]

Given that A+B=[[2,5],[7,8]] and A-B=[[6,8],[4,3]] Find 2A .

If * is defined by a * b=a-b^2 and oplus is defined by a oplus b = a^2+b ,where a and b are integers.Then find the value of ( 3 oplus 4 ) * 5