How do you multiply #((2, -1), (3, 4))^4#? Precalculus Matrix Algebra Multiplication of Matrices 1 Answer Ananda Dasgupta Mar 22, 2018 #((-107, -84),(252,61)) # Explanation: Just like with ordinary numbers #A^4 = A times A times A times A#. This looks like it may take three matrix multiplications, but we can actually do this in 2. #A = ((2, -1), (3, 4)) implies# #A^2 = ((2, -1), (3, 4))((2, -1), (3, 4)) = ((1, -6),(18,13))# and thus #A^4 =A^2 times A^2 = ((1, -6),(18,13))((1, -6),(18,13)) =((-107, -84),(252,61)) # Answer link Related questions What is multiplication of matrices? How do I do multiplication of matrices? What is scalar multiplication of matrices? What are some sample matrix multiplication problems? How do I multiply the matrix #((6, 4, 24),(1, -9, 8))# by 4? How do I multiply the matrix #((3, 0, -19),(0, 7, 1), (1, 1/5, 2/3))# by -6? How do I multiply the matrix #((6, 4, 24),(1, -9, 8))# by the matrix #((1, 5, 0), (3, -6, 2))#? Is matrix multiplication associative? If #A=((-4, 5),(3, 2))# and #B=((-6, 2), (1/2, 3/4))#, what is #AB#? In matrix multiplication, does ABC=ACB? See all questions in Multiplication of Matrices Impact of this question 1810 views around the world You can reuse this answer Creative Commons License